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DOCUMENT RESUME

ED 066 875

EM 010 151

TITLE

INSTITUTI ON

SPONS AGENCY
PUB DATE
NOTE

Proceedings of the 1972 Conference on Computers in
Undergraduate Curricula.

Georgia Inst, of Tech., Atlanta. ; Southern Regional
Education Board, Atlanta, Ga.

National Science Foundation, Washington, D.C.

578p.

EDRS PRICE MF-J0.65 HC-$19.74

DESCRIPTORS Art Education; Biology; Business Education;

Chemistry; *Computer Assisted Instruction; Economics;
Education; Engineering; Geography; Interinstitutional
Cooperation; Language Instruction; Mathematics;
Physics; Social Sciences; Speeches; Statistics;
Teacher Education; Undergraduate Study

ABSTRACT

The 83 papers presented at the 1972 Conference on
Computers in Undergraduate Curricula are reproduced in this volume.
With computer science specifically excluded as an area of interest
for the conference, papers fall under the following headings:
biology, business, chemistry, economics, education, engineering,
geography, languages and art, mathematics, physics, social sciences,
statistics, and a general section on faculty training, software
exchange, and shoestring facilities. (RH)

Proceedings of the
§ 1972 Conference on Computers

' 1 in Undergraduate Curricula

1 1 1

June 12, 13, 14, 1972 Atlanta, Georgia

Sponsored by the Southern Regional Education Board

in cooperation with the

Department of Continuing Education, Georgia Institute of Technology

Proceedings of the
, 1972 Conference on Computers
- in Undergraduate Curricula

June 12, 13, 14, 1972 Atlanta, Georgia

Sponsored by the Southern Regional Education Board

in cooperation with the

Department of Continuing Education, Georgia Institute of Technology
wits support from the
f.ational Science Foundation

U.S. DEPARTMENT OF HEALTH.
EDUCATION & WELFARE
OFFICE OF EDUCATION
THIS DOCUMENT HAS 8EEN REPRO-
DUCED EXACTLY AS RECEIVED FRO*,.
THE PfiRSON OR ORGANIZATION ORIG-
INATING IT POINTS OF VIEW OR OPIN-
IONS STATED DO NOT NECESSARILY
REPRESENT OFFICIAL OFFICE OF EDU
CATION POSITION OR POLICY

Library of Congress Catalog Card Number 72-83189
Printed in the united Jtates of America
Distributed by

the Southern Regional Education Board, Atlanta, Georgia

CONTENTS

lusmusiM EAUifcs

Nillian F. Atchison, University of Maryland
Mfleport on Inter Qtti onal Pannls”

blOLDGl

SIMULATION OP BIOLOGICAL 5 I STEMS# I

Chairnan, Nary Jane Brannon, Huntingdon College

Thoias L. Iseahour, University of north Carolina

John C. Marshall

Howard D. Orr, St. Jlaf Collage

HThe Use of the Conputer in an Undergraduate Ecology Course”

Stephen B. Kessell, Aeherst College
"Quantitative Ecology for Undergraduates”

Howard c. Howland, Cornell University

"Digital and Analog Conputing in General Aninal Physiology”

SIMULATION OF BIOLOGICAL SISTERS, II

Chairnan, Mary Jane Brannon, Huntingdon College

Ernest H- Salter, Cottey Junior College for tfonen
Bar.ry L. Batenan

Gerald N. Pitts, University of Southwestern Louisiana
HConputerized Ecology Simulation"

Davis S. Hinds
Mary Ellen Burrows

Janes c. Horton, California State College
"Computer Based Ingairy Investigations in Biology”

BUSINESS

BUSINESS AND ACCOUNTING

Chairnan, B. G- Duna, faireont State College

tfillian F. Bentz, University of Kansas

"Computer Assisted Algorithn Learning in Accounting”

Thomas L. Guthrie, Indiana University at Port Uayae
"The Business Core Integrator at Indiana University”

Elbert B. Greynolds, Jr., Georgia state University
"The Tine-Sharing Conputer and Intermediate Accounting”

Harley H. Courtney, University of Texas at Arlington
"fieoote Tine-Sharing for Education in Business Planning and
Control"

cHBHisray

CAI IN THE CHEMISTS Y CLAS3B00H

Chairnan, Charles Merideth, Ho rehouse College

J. J. La go wri i
S. J. Castleberry

G. H. Culp, University of Texas at Austin

"The Inpact of Conpu ter-Based Instructional Methods in

General Chenistry"

Bonald W. Collins, Eastern Michigan University

"Computer-Aided Classroom Chemistry Instruction Vim
Instantaneous Video Projection of Teletype Output"

V. F. Sliwinski

K. J* Johnson,, Univarsity of Pittsburgh
"Pitt's Interactive Graphics and Computer-Gemerated
' Repeatable Examination Systems"

INSTRUCTIONAL PROGRAMS IN CHEMISTRY

Chairman, Harris Burns, Jr*, Randolph-Macon College

Joyce H* Corrington, Xavier University
Lee P* Gary, Jr.

L* Chopin Cusachs, Loyola University

"Interfacing Students and Computing Through Undergraduate
Chemical Research"

Uon&ld 0* Crain, Oniversity of Kansas

"A CAI Program for Aromatic Organic Syntheses Written in
Tiae-Sharing FORTRAN *

Alfred J* Lata, University of Kansas

"An Interactive Tima-Sharing Basic Tutorial Program

Sequence in Introductory Electrochemistry"

ECONOMICS

ECONOMIC AND BUSINESS SIH3 LATION/GAHING

Chairman, Donald Chand, Georgia State University

Donald P* Cole, Drew University
J« william Hanlon, Winona State College
"Micromod: Description, Use and Evaluation of a

Microeconomics Computer Game"

James D. J. Holmes, St* Andrews Presbyterian College
"New Approaches to Business Simulations"

Ray Billingsley

Stanley Wilson, Texas A £ M University

"Computer Simulation of Economic Models for Instructional
Usage"

ECONOMICS

Chairman, Martin Solomon, University of Kentucky
Fiank J* Bonello

William I* Davisson, University of Notre Dame

"Computer Assisted Instruction in Economics at the University

of Notre Dane"

Frank DePelice, Beliont Abbey College
"Integrating Computar Programs in Economics
via Time Sharing Terminals"

Richard A* Stanford, Furman University

"Ceteris Paribus Methodology and Computerized Economics- Business
Models"

EDUCATION-CAI-CHI

Chairman, Sylvia Chirp, Philadelphia Public Schools
Carol A* Cartwright

G* Philip Cartwright, Pennsylvania State University

"An Undergraduate Computer- Assisted Instruction Course in the

Early Identification of Handicapped Children"

Roger H* Geeslin, Univnrsity of Louinville
"Preparing Mathematics Teachers to Use the Computer in
Secondary Schools*

Joan Straughan

Raymond F. Latta, Wistern Washington State College
"Conputer-Nanagnd las tract ioa: A Beginning and a Reality at

Western Washingtoc State College"

SUPPORT OP X MOXf ID U A LIZ ED XISTIUCTIOR

Chairman, Henry T* lippnrt, OSA Medical field Service School

Harold L* Schoen, Virginia Polytechnic Institute
"A Coaparison of Types of feedback to Student Responses in a
CAI Unit"

Arthur Wagner

Ronald Bleed, Joliet Junior College

"Using a Conputer to Support the Testing Progras in

Audio-Tutorial Biology"

Gail N. Nishinoto
John fl. Horowitz
Ray E. Burger

Richard P- waiters. University of California at Davis
"Initial Development of Individualized Instruction with
Conputer Support"

MANAGEMENT OF EXAMINATIONS AND LARGE ENROLMENTS

Chairman, Henry T« Lippert, USA Medical Field Jervice School
C« Obert Henderson

Nark Haaaer, Washington State University

"inproving Large Encollsent Undergraduate Instruction with
Conputer Generated, Repeatable Tests"

Stanley J* Birkin, University of SoutL Florida
"An Analysis of the Use and Effectiveness of EZARINER: A

Cosputerized Question Bank and Ezasination Processing Systee *
in College of Businass Courses at the University of South Florida"

fcU ~G« Franke
W« D- Dolphin

G« p. Covert, Iowa State University

C. D. Jorgensen, Brighan Young University

NA Con pu ter- Assisted Method for Teaching Large Enrollment

Lecture Sections: The Biology Phase Achievement System (PAS)"

Michael Baldigo, Indiana University School of Business
"Operational Aspects of Computer Written and Scorud First Year
College Accounting Progress Examinations"

ENGINEERING

ENGINEERING COURSES

Chairman, Rufus F- talker, Jr*, Centenary College of
Louisiana

Tadao flurata

Boland Priener, University of Illinois

"On the Use of a Coiputer for Motivating student Projects in
Undergraduate Courses on Network Theory"

Arthur Houghton
George H* Quentin

Bruce R. Peterson, University of New Mexico
"A Course in Conputer Simulation and Analysis for
Scientists and Engineers"

177

183

189

195

199

207

217

221

229

235

241

2 49

Donald C. Aaoss

John N. Gowdy# clnason Univecalty

"Realization and Cltssrooa Application of a Display- Based
Syatea Cor a saall Digital Coaputer"

ENGINE SUING APPLICATIONS

Chairaan, Bernard Rtigaan, Loyola College

Paul T. Borlarty, van York City Coaaunity College
"Coaputer Assisted Suaerlcal Control Part Prograaaing"

N. tfaverly Grahaav m

Don S. Haraer, Georjia Institute of Technology

"An On-Line Binicoaputer in the Nuclear Engineering Cltssrooa"

Uichard Schubert

Joseph H. Gill# Nestern Hichigan University

"Coaputer Applications to Kineaatic Synthesis of four Bar

Mechanises"

Hinrich 8. Nartens

Stephen G. Margolis, SUNT# Buffalo

HAn Analog Coaputer Optimized for Undergraduate Instruction"

GEOGaAPHY

GBOGBAPH Y

Chairaan, A. A. J. iioffaan, Texas Christian University

Philip H. Lankford, University of California
"Spatial Bodel Builling in the Social Sciences"

Vincent H. Balstroav Middlebury College

"The Coaputer in Uniergraduate Geography at fllddlebury"

Paul E. Lovingood, Jr.

David J. Coven, University of South Carolina

"The Use of Coaputers in Geographic Instruction as a Beans

for Stiaulating Interest in Statistical Bethods"

Nancy B. Hultquist, University of Iova

"Introducing Undergraduate Geographers to Quantitative

Analysis Through a B egionalizatioi Praaevork"

LANGUAGES AND ABT

LANGUAGES AND ART

Chairaan, Haskell Siapson, Haapden-Sydney College

Anna Barie Thanes, Joldea Vest College
"CAI and English: A Tentative Helationshi p"

Robert Phillips, BAiai University

"Drilling Spanish Varb Foras on Beaote Teraiaals"

Grace C. Hertlein, Chico State College

"Coaputer-Aided Graphics as an Art Fora for the Artist"

wias allies

MATHEMATICS I

Chairaan, G. P. tfeeg, University of Iova

Thoaas Bailey, The Jhio University

"Use of the Coaputer in Introductory Algebra"

255

265

273

277

285

291

295

299

305

311

317

321

325

Allen D. Ziebur, Stite University of lev fork
m A Tiaa-Sharing Coaputer in tka Diffaraatial Equations
Course"

(I. M. flcAHistar , floravi.an Collage 329

"Tka Bole of tha Coaputor in Baal Analysis"

(1ATHEI1 AT ICS It

Chairaan, Gar a id L. Engal, Pennsylvania State Univaraity

Arthur E* Falk 335

Bichard Bouchard, Wtatara Bichigan Univaraity
"Coaputerizad Halp ia Pindiag Logic Proofs"

Doainic Soda 343

Aaron H. Koastaa

Judith Johnson, Tha Liodenuood Collages
"Coaputors, Clay and Calculus"

Everett Hainer, Raapshire College 349

"APL at Haapshire"

Roger B. Kirchner, Car let on Collage 359

"Coaputer Generated Pictures Cor Teaching Calculus"

EdlSICS

QUANTUB PH TSICS

Chairaan, Bayne Lang, flacffurray Collage

Carol Bennett, univarsity of Illinois 369

"coapu ter-Based Education Lessons for Undergraduate Quanta*

Mechanics"

John flerrill, Dartmouth College 375

"Introductory Quantua flachanics and the Coaputer"

COAPUTER GRAPHICS AND PHTSICS

Chairaan, Arthur Lushraann, Dartaouth College

David Grillot 383

JeCCrey D. Ballance

Larry B. Hubble, Origon State University
Tie. G. Kelley, Southern Oregon collage
"Interactive Classroom Graphics"

Herbert Peckhaa, Gavilan College 397

"Coiputer Graphics in Physics"

Alfred Bork 409

Richard Ballard, University of California at Irvine
"Coaputer Graphics ind Physics Teaching"

PHTSICS

Chairaan, Alfred Bork, University of California at Irvine

Harold tfeiastock, Illinois Institute of Technology 417

"Statistical Physics Coaputer Applications"

Charles P- (lunch. University of California at Irvine 427

"An Interactive Coaputer Teaching Dialog for Solving a
System of Coupled Oscillators"

W. E. Bron, Indiana Oniversity 433

"Project CAPLIH: Coaputer Aided Physics

Laboratory Instruction for Bon-Science Bajors"

vii

IKllk iZlMilS

H£S ART

Chairaan, Joseph Rtban, Qaaais Collago

Betty L. Jeho, University of Daytoa 439

"A Coapu ter- Assisted Instruction Program in Aaa^icaa
History , 187 0- 192 1**

Charles a. Dollar, Jklahoaa State University 449

"A Preliminary Sapoct oa Coapu tar- Assisted Learning in
Aaerican History Courses at Oklahosa State University"

POLITICAL SCIENCE

Chairaan, Calvin Hiller, Virginia State College

Williaa 0. Coplin 459

Bichael K. O’Loary, Syracuse Univorsity
"Educational Uses of PRINCE"

Bruce D. Bowen 463

Wayne K. Davis, The University of Hichigan
"VOTES: A social Science Data Analysis Prograa”

Janes E. Harf, Ohio State Univarsity 467

"A Student Handbook of Eapirical Evidence: The

Utilization of CAPE Data in Undergraduate Education"

SOCIAL SCIENCE I

Chairaan, Honald Stiff, Illinois Institute of Technology

Daniel Vandepor taela 477

Honald Stiff, Illinois Institute of Technology

"The Creation and Diffusion of Innovative Uses of the

Computer in Sociology Edncation"

Joseph &• Denk, N . Educational Computing Service 483

" POISSON — A Daughter of Dartaouth*s IMPRESS Has Been Born
in the Environment of IBH Tiae-Shar ing"

Thoaas P« Kershner, Union College 489

"Computer Applications for Social Scientists"

SOCIAL SCIENCE II: SlflUUTlON

Chairaan, Jaaes Hogge, George Peabody College

Arthur 0, Croaer 493

John B- Thuraond, Uaiversity of Louisville
"Toward the Optiaal Use of Coaputer Simulations in
Teaching scientific Besearch Strategy"

John Bartholoaev 495

Judith Johnston

Aaron H« Konstaa, The Lindenwood Colleges

"A serious Gaae as in Introduction to Urban Planning"

Marshall H. Whithed, Teaple University 505

"Political siaulation and the Hini-Coa pu ter* • • A Challenge
to the Industry"

srAXtsii£s

STATISTICS I

Chairaan, Williaa G. Bulgren, University of Kansas

Elliot A. Tanis, Hope College 513

"Theory of Probability and Statistics Illustrated by the

Coaputer"

viii

Hare S. veins, vaakiagton Stata Daiveraity
"PSYSTAT--A Teackiaj Aid Cor Introductory St# .iatica"

Herbert L. Darahea, Hopa Collage

"A Course oa Coaputlng and Statiatica Cor Social Science
Studeat a"

STATISTICS II

Chairnan, David G. deinnan, Bolliaa collage

S. c. Uu, California State Polytechnic Collage

"An Altarnatifi Approach in ranching Statiatica! Methoda"

Frederick S. Halley, SONY, Brockport
"Individualized laatructioa in Baaic Statiatica: An

Expariaant in Coaputar Managed laatructioa"

Robert Platcker

Clark I. Guilliaee, diaaouri Soatkara State Collage
"Through Multiple Bagraaaion aad Thraavay AI0V in Sopkoaora
Level Applied Statiatica for tka Behavioral and Natural
Sciences: Instructor-Student Daaoaatral.ion of the darchant

Cogito 1016 PBalOTA - 2"

5EeS5Afc

FACULTY TRAINING AND SOPYIAIE EXCHANGE

Chairnan, Judy Edvards, Northwest lagional Education
Laboratory

Joseph R. Dank, North Carolina Educational Coaputiag Service
"CONDUIT — A Concrata Pipeline for Sof t vare-S tac ved Little
People"

Ronald L. Code, Stanford Univaraity

"An Experinent in Coaputer Training for Collage Faculty"

L- D. Kugler

J. N. Snider, Univarsity of Hickigan at Flint

"Friendly Persuasion: Initiating Reluctant Faculty to the

Coaputer in the claasrooa"

SHOESTRING FACILITIES

Chairnan, Herbert Packhan, Gavilan College

0* Tkoaas Bass, Macon Junior College
"A Conputerized Physics Laboratory”

Don Leslie Levis, Bae County College

"Heasureaent of an lutoaobile's Fuel Consuaption, Road
Horsepower, Maxiaua Speed and Maxiaua Acceleration"

John P. Tucciarone, St. John's University
"Infinite Sequences and Series Via the Coaputer"

521

525

52 J
533

539

547

555

567

575

577

585

FOREWORD

This proceedings is for the third of a series of conferences on computer uses m
un lot gca dua te curricula supported by the National Science Foundation through its Office or
:oipj tiny Activities. The 1970 Conference was sponsored by the University of lova and the 1971
Conference by Dartmouth College. The 1972 conference was planned by a national steering
cono) ttee consisting of Gerai- L. Engel, Pennsylvania State University (ou leave froe Haapden-
Syin?y College), Joh*i W. Haablan, Southern Regional Education Board, Glenn R. Ingraa, Washington
State University, Thoaas E. <urt* , Darteouth College, Gerard P. Weeg, University of Iowa and
PraJ W. wemgart*»n, Clareaont Colleges*

Eighty-th^ee (B 3) papers wire selected by panels of referees icon the 17J papers sent in cor
consideration and are reproduced in the following pages. We are indebted to Jerry Engel for
organizing and administering the paper selection process and to uleno Ingram tor preparing the
"Call foi Papers."

Computer Science was specifically excluded as an area of interest for the conference.
Papers on computer services ara included only if they have novel features or if the services are
lnciiental to other topics.

This docuaent was prepared using the ATS ( Ad am istrati ve Terainal Systea) with the IBM
Jbd/SO coaputer in the Inforaation Pocessing Systeas Department of the Alanta Pubiic Schools.
The text was entered into the coaputer via NOVAR terminals by the Vision Center of Atlanta
Public Schools. The splendid cooperation obtained froa Thoaas McConnell and Marion Boyles,
aeids of these two departments, respectively, was essential in carrying out this hu;a task*
Particular recognition of Linda Reagan of the Vision Center is due tor her constant
participation in the typing ot the papers and the corrections, to Edward Peabody who did all of
the paste-up work associated with the preparation of tne carneta-ready copy, to Myra Peabodv and
her friends tor the aany sours they devoted to proofreading and to Wade Royston, SRE3
Publications Assistant, tor his guidance.

Tnroughout these proceedings you will find several designs created by the students of Grace
C. Hcitlein (see her paper p. 317) in her course Coaputer- A^ed Gjraph ±cs as ait Art Fopa at Chico
Stita College. They afforl i pleasant break ia the aonotony ot the printed page and we are
grateful tor them.

The papers were assuaed to be ready for publication as subaitted and editing was done only
m extreme cases. Every atteapt was aade not to introduce errors in spelling, typing, etc.
during the copy preparation process. In doing so we have discovered and reaoved soae ot the
authors4 preparation errors. We hope that the end result is at least no worse for having passed
tnrojgn our hands - indeed we believe that the net result of our efforts is on the laproveaent
s ide.

To enhance future coai l n icat ion between the readers and the authors ve have included the
telephone number of the author when it was available and a concerted effort was aade to furnish
the zip ('ode. Tae reward for our efforts will depend upon how you, the reader, and the
conference participants are able to benefit froa these proceedings, the conference
presentations, ana what are usually the aost valuable - the mtoraal discussions and personal
contacts which are afforded >y such gatherings ot highly motivated persons.

Tne local arrangements for the 1972 conference were made with the assistance of the
Department of Continuing Education, Georgia Institute of Technology, under the direction of
^lchiri Wiegand, and its st ff, particularly, bob iierndon and Ken Collins. The chairaan was
also assisted by a Local Hosts committee consisting of luell Evans, Emory University, Thoaas
McConnell, Atlanta Public Schools, Bob Pearson, University System of Georgia Coaputer Network,
Vladimir Slatueck*, Georgia Institute of Technology, Grover Siaaons, Atlanta University Center
Corporation, and William Wells, Georgia State University. The extensive effort devoted to the
planning and operation of the "Coaputer Pair44 by Bob Pearson and his staff deserves special
mention as does also Suzauna Bowaan, the Chairaan* s Secretary, for her dedicated attention to
coaau nica ti ons and registration.

Finally, this series of conferences would not have been possible without the unswerving
belief that the coaputer can and should be used to iaprove the guality of undergraduate
education which is neid by Arthur Melaed and Andrew Molnar of the National Science Foundations
Office of Coaputing Activities, their enc our ageaent and their support. Nor would the
conferences be possible without the contributions by the many authors, referees and attendees.
To these we express our gratitide and hope that theii rewards are aany.

John W. Haablen

1972 Conference Chairman

3EP0BT OR THE I RTEBtf ATIOIAL PAIELS

Villiaa P. Atchison
University of Maryland
College Park, Maryland 20742

A group of twelve speakers froa other countries have bean invited to taka part in panel
discussions at this conference. Each will give a report on soae aspect of the use of coaputara
in his country, soae speaking on applications of coaputers in various subjects and others
speaking aore directly on coaputer science education at various levels. All acxbers of the
group are involve*! in education and the use of coaputers in secondary schools, and aore
particularly, all are interested in the training of teachers for secondary schools. At the
conference there will be two panel discussions * "Coaputer Applications in the Sciences Abroad,"
and "The Status of Coaputer Education in Other Countries. w

Poliowing the conference, the group is going to have a workshop to prepare aaterials for a
new booklet entitled "Aias and Objectives of Coaputer Studies in General Educatiou" describing a
college course tor the training of secondary school teachers of: coaputer education. This work
will be an extension of the International Federation for Inf oraai.ion Processing (IPIP) booklet
entitled, "Coaputer Education for Teachers in Secondary Schools, An Outline Guide," published by
tha IPIP Working Group on Secondary School Education (KG 3.1) in Septeaber 1971. This nex
booklet will be the first in a series of booklets to be published jointly by WG 3.1 of IPIP and
tha Organization for Econoaic Cooperation and Developaent (OECD). The panel discussions and the
work on the new booklet is a joint effort of IPIP and OECD and is sponsored jointly by the
National Science Poundation and the U. S. Office of Education. A brief listing of the speakers,
along with a coaaent on their reports and background, is given below.

Alfred &££<!§£ froa Vienna, Austria is Head of the Austrian School Coaputer center,
lie works on courses for pupils in secondary schools, courses for post secondary
vocational training and courses for teachers. The Center also does adain istrative
work for the Ministry of Education including the establishment of data banks of
teachers of secondary schools and data banks of pupils in one section of Austria.
His panel presentation will be on "The lapact of Coaputer Science on the Teaching of
Matheaat ics. "

Glen Bonhaa, froa Toronto, Canada, works for the Departaent of Education. He has been
a teacher~and is now involved in the developaent of coaputer science ind data
processing courses for teachers. He will report on "Confuting in the Shools of
Ontario, Canada." He will describe secondary school courses and how they relate to
University courses and also report on soae education research projects.

Utje Brondua is froa Copenhagen, Denaark, where he works in the Offices of the
Directorate for Vocational Education. He has helped plan the developaent of coaputer
education in the Danish educational system. He is in a good position to give the
latest news about the state of the art in coapurer education in his country since he
recently lectured on this subject in Denaark. The title of his talk is "A Report on
Activities in the Field of Coaputer Education in Denaark."

Is. Garcia caaay \ ro froa Madrid, Spain is on the staff of the Coaputing Center at the
University of Madrid. He teaches courses in inforaatics and is interested in
prograaaing languages and coaputer education at the secondary level. He has been a
speaker on coaputer education at aany international conferences and will report to us
ou coaputer education in Spain.

Jacques Hgbgngt reit is froa Par it- , France. He teaches inforaatics at the Ecole
Superior d • Electnici te and at the University of Paris. One of his aain theses is that
the ideas of inforaatics should be eajedded in the teaching of aany subjects. He has
played a key role in the training of large groups of teachers for secondary schools.
The title of his talk is "Teacher Training in Inforaatics in General Secondary
Education in France." He ^s selected to be the prograa chairaan for the Second World
Conference on Coaputer Edu ation to be held in France in 1975*

jfldfe Kiychber uer of Paris, France will chair the panel discussion on "Coaputer
Applications in the Sciences Abroad." He has played an integral role in a nuaber of
international seainars and conferences particularly in the area of coaputer education
at the secondary level. He has helped to coordinate the international aspects of this
conference. Dr. Kirchberger works for the Centre for Educational Research and
Innovation of the Organization for Econoaic Cooperation and Developaent (OECD) and is
in. a unique position to speak not only of developaents in France, but also of
international cooperation.

R. froa Bridges Place, London, United Kingdoa, is i. lecturer in
aatheaatics at Chelsea College of Science and Technology, a branch of the University
of London. He i.s assisting in the developaent of new science courses which are based
on learning and understanding by discovery. Experiaents are siaulated on the coaputer
and jiaulation packages are aade available to pupils via interactive terainals. He
his a background in physics as well as aatheaatics and is the Director of an
associated coaputing project. The title of his talk is "The Developaent of Sianlation
Packages for the Teaching of Science. "

&*. Lgvjs is froa Walton, Bletchley, Buckinghaashire United Kingdoa. He is on
the faculty of The Open University and is developing curriculaa aaterials for
coaputer education. He gave a paper at the Seainar on Coaputer Sciences in Secondary
Education held at Savres, Prance, March 9-14, 1970, entitled "Teacher Training and
Retraining in Coaputer Sciences.14 The concepts and innovative aethods of The Open
University have received auch publicity and vide acclaia. fir. Lovis will give a
report based on his own experiences with The Open University.

Xil2 Malpbep g, froa Uppsala, Sweden is with the Departaent of Education and is
interested in educational technology as well as coaputer education. He took part in
the CEB 1/OECD Conference on Coaputer Sciences in Secondary Education held in Paris,
France during Juno 21-25, 1971. He will report on the developacnts in coaputer
education in Sweden.

g* Jagg is :roa Bailrigg, Lancaster, United Kingdoa. He is a senior lecturer in
the Aatheaatics Departaent of the University of Lancaster, conducting a course in
Coapater Oriented Aatheaatics for Students of Biological and Social Sciences, and
chairing the Aatheaatics panel in the School of Education. He has spent thirty years
as a aatheaatics teacher, having introduced coaputer studies starting in 1957. He was
Chairaan of the British Coaputer Society Schools Coaaittee froa 1966 to 1970. The
title of his presentation is NSoae Varieties of Approach to the Teaching of Coaputer
Studies to Undergraduates."

J. 2*. Tinsley is fraa Manchester, United Kingdoa and is currently Head of the Schools
Project of the Rational Coaputer Center. His background is in aatheaatics, and he has
been - teacher for a nuaber of years as well as being Head of the Aatheaatics
Departaent at St. Edwards School of Oxford. He has been an active aeaber of the
British Coaputer Society Schools Coaaittee as veil as an active aeaber of the tFIP
wording Group on Seoordary Education (VG 3.1). He will report on "The Present
Situation in Collages and Departaents of Education in England and vales concerning
the Provision of Courses of Coaputer Studies for Trainee Teachers."

Dt Henk Wolbeps is froa Voorschoten, Netherlands. He is currently Professor of
Xnforaation at the Technological University at Delft and has served as Director of
the Coaputer Center at Delft. His original training was as an electrical engineer. He
has been very active on international coaaittees in coaputer science education and is
a aeaber of the EPIP Technical Coaaittee for Coaputer Science Education (TC 1) and
the Uorking Group oa Secondary Education (VG 3.1). The title of his talk is
"Coaputers in the University Curriculua in the Netherlands."

The workshop on the preparation of the booklet "Aias and Objectives of Coaputer Studies in
General Education" will also have five representatives froa the United States assisting. Each of
these is well-gualif ied to contribute to this effort on the training of secondary school
teachers. They are:

Chairaan of the IFIP Working Group on Secondary Education (VG
3.1) and Director of~the Coaputer Sience Center at the University of Maryland.

Sylvia Char r, a member of VG 3.1 and Director of Instructional Systems for the School
District of Philadelphia.

Jgdy ffdwards froa the Northwest Regional Educational Laboratory, Portland, Oregon.

David Ct Johnson froa the Matheaatics Education Departaent of the University of
Minnesota.

Thoias Dgye£ froa toe Coaputer Science Departaent at the University of Pittsburgh.

THE OSE OP THE COHPUTEH IN AH
UN DERG H ADU AT E ECOLOGY COURSE

Joha C. Marshall and Howard D. Dr r
Saiat Olaf College
Northfield, Minnesota 55057

Thoaas L. Isenhour
University of North Carolina
Chapel Hill, North Carolina 27514

I fttrgdoct^gn

One of the difficulties encountered in teaching an undergraduate ecology course is finding
ways to adequately demonstrate and apply the theory. For example, it is possible to construct
aolels of population interactions which deaonstrate how a seif regulating ecological system such
as a forest may develop. But to demonstrate the functional dependencies that are important in
su:h models is somewhat more difficult. Furthermore, the time interval for developmental change
or response to perturbation in natural systems is frequently too long to make significant
observations to support all or even significant parts of most theoretical models during a one
semester course. This is particularly true in northern latitudes where *he duration of the field
worn is limited by the weather. This report concerns our experience with the use of several
coiputer programs \v.o supplement a one semester undergraduate couLse in ecology. Testing seems to
indicate that the use of tha computer for gaming in the areas of population dynamics and as an
aid to the field analysis of community structure has resulted in a significant enrichment in the
ecology course. The programs presently in use are part of a large collection of programs,
ranging from very simple to quite complex, and designed to encourage undergraduate biology
studants to learn to program.

Iha Course Organization

In lecture the course starts with conceptual examination of eco-systems in terms of overall
function in relation to structire. This logically leads to a detailed examination of unit parts,
populations, and the isolation and discussion of them. Thus, in general, the flow of the course
is initially reductionalistic, leading to a focus on the species populations. At this point the
detailed study of population dynamics using computer "exper iments" is introduced. Programs
illustrating population growth, limited and unlimited, population regulation, competition,
predator-prey and a simple acosystem are made available to the students. These programs allow
tha student to experiment with parameters and functional relationsips and thereby gain a feeling
for the nature of the traditional mathematical models of population dynamics. The programs used
quits logically introduce the student to a synthetic approach, culminating in a computer model
of a simple ecosystem.

Concurrent with the lecture, the laboratory is centered around a study of community
structures using natural ecosystems. Here the computer is used to process data from field
collections on a day to day basis, encouraging hypothesis testing and making possible rapid
modifications in experimental design, while studies ci natural communities are in progress.

In summary, two general areas of computer application have proven highly significant in an
undergraduate ecology course. First, programs simulating population dynamics have allowed the
student to examine for himself the effect of certain population parameters over a period of many
generations. These simulation 3tudies lead to an experimentation with a systea model, which
sharpen concepts in application of theory to management of ecosystems. Secondly, a unified
laboratory study of community structure has proven successful using the almost instant data
processing of collection data to modify the work as it proceeds. These two points will be
discussed in some detail below.

Program

Our experience indicates that generally less than one-fourth of the students who register
for undergraduate ecology have had previous computer experience of any kind. This reguires that
very explicit input directions be given for each of the programs as no attempt is made in the
course to teach programming, tfxile the ecological implications and limitations, of each of the
models is discussed in lecture, no attempt is made to explain details of coding. All the
programs used are written in FORTRAN and are given the status of system programs while the
ecology course is in session.

The use of the simulation programs is timed to correspond with and support the discussion
of population dynamics in lecture. Special emphasis is given to the effects of key parameters
that can be input to the computer models we have. The student is then asked to game, examining.

to his ova rati sf ac t ion , the affect of varying population regulation parameters. All the
programs are designed to accept any nuaber of sets of input and to print out, for each set of
input, a record of population iensity as a function of tiae or the nuaber of iterations,
whichever is appropriate.

The laboratory prograas are Jsed primarily to analyze field data, but are presented in such
a vay as to encourage experimeatal design prior to data collection.

orj. Population Dyn aa^cs

The coaputer aodels used in support of lectu r e- d iscussion of population dynamics, listed in
their order of presentation to the students are

1. Model of unlimited growth

2. Model of liaited growth

3. Model of self-regulation

4. Model of competition

5. Model of predator-prey

6. Model of a simple ecosystem

1* he first two programs are praLiainary in nature respectively utilizing the relationships

^ = rN

(1)

zr = rN(l-N/K)
dt

(2)

Whare N is the population at tiae T, r is the reproduction rate constant and (eguation 2) K is
the carrying capacity of the environment. These two aodels demonstrate numerically the
explosive prediction of equation (1) and the sigaoid prediction of equation (2).

The third model
population model that
pressure on the pop
following situations:

is based on a treatment by Smith[ 1 1 and quite adequately presents a
includes an input parameter (K) , which is indicative of the regulatory
ulation. By variation of this parameter the student can demonstrate the

K-0 the population will increase without liait

0<K<1 population will reach eguilibriua without oscillation

1<K<2 population equilibrium will be approached with oscillations of

decreasing magnitude

K>2 the amplitude of the population osdillation will increase

without limit

X ho fourth program presents a aodel of the competition of
:lassical description of Sause[2] i. e. which may be stated as follows:

two species based on the

ar s riVKi-MraN2)/Ki

(3)

dN.

dt1 = r2M2(K2-VbNl)/K2

(4)

Where a and b are coefficients that respectively state the effect of species 2 on species 1 and
the effect of species 1 on species 2. The values of r, K and N are respectively the reproductive
rate constant, the carrying capacity of the environment and the initial population for the two
species. The students input wiat they consider appropriate values for the parameters in
equations (3) and (4) and the program outputs the population levels for the two populations a r a
function of time, tfe have found this to be a very effective way to illustrate clearly this
model, which, without illustration is largely concealed by the complexity of the two
simultaneous differential equations.

The predator- prey model used is a modification of the treatment presented by Spain[ i ] and
well described by him. The student learns a great deal about predator-prey interaction both from
consideration of the numerous factors that must be specified on input and the examination of the
graphical output of the prograi.

ierJc

Following experience with the five programs above the student is introduced to a program
that attempts to implement many of the ideas he has learned into a model ot a simple ecosystem
with three trophic levels. The required input for each trophic level is as follows:

Ei*fits: initial population, probability of "birth", probab

of destructioa by herbivores, optinua space requirements

initial popilation, probability of birth, probabi

probability of eating, probability of being eaten, nua
necessary for starvation, optiaua space requirements.

£®£!iil2E®§- initial popJlation, probability of birth, probabi

probability of eating, probability of death by coabat,
necessary for starvation, optiaua space regu ireme n ts.

to specify the area in which the system
ion and emigration. The probabilities s
Le of the aodel and are in terns of the
: level. Bach population event is indivi
certain type are evaluated as illustrated
has a coaputed probability (based on the
non-optimum population levels) of 0.5
:e three possible outcomes, no event, one
interval. Th? probabilities for each of the three possi
cients of a three term binomial expans
an be used for a population of any rea
ccur within a given population of N in
by computing the probability that the event will occur to an individual,
between 0 and 1 and sumaing th* normalized coefficient of the binomial e
until the summation is equal or greater than the random nuaber. The nu
is then taken as one more than the number of normalized binoaial terms s
for zero events). A typical output of this program is shown in Table t
levels input for this case are plants, 2500, herbivores, 500, and carniv
has proven useful as a vehicle for the illustration of modelling. The
quite adequately illustrate the nature of a simple ecosystem. Finally,
Students have been observed leaning over the printer shouting words of
the trophic levels threatened with extinction.

aodel requi

res

the user

ui ed

to be

closed

to iamigra

at e 1

:o t he

a r b

i t ra

ry time sc

iv idi

lal within

a g

iven troph

al i

lumber

events of a

tuple.

. Cons

ider

a n

event that

s e i

lent

a nd

mod

ifiod at

iv idi

lals.

This

mea

ns there i

hi n

a time

in te

rval. Tha

i ved

f rom

the

norm

alized coa

.25, (

). 50,

0.25

. Th

is argumafi

ev ent

is of

a ce

rtai

n type thi

ty of
s

death ,

proba bil

ity

lit y

of nat

ural

dea

th.

ber o

f time

t er v

als

lit y

of nat

ural

dea

th.

nuaber

of time in

t er v

als

exist

s a nd t

his

area

v r*

pecif i

ed for

each

en t

e ven t

probabi

lit y

for

a n

dually

evalua

ted

and

the

by t h

e folio

wing

si m

pie

input

probabili

for

and a

popula

t ion

two

event

* or

two

a ve

n ts

ble ou

tcomes

can

then

ion an

d a re r

espe

ct i v

ely

sonable size.

The

nua

ber

di vid u

als is

evalua

ted

draw i

ng a ra

ndom

nua

ber

xpansi

on for

N ♦

1 t e

rms

mber of event

s oc

cur r

ing

ummed

(the fi

r st

term

. The

optimum

populat

ion

ores.

50. Th

program

result

s from

the

prog

ram

the

prog ra

a i

s f

un.

encou

ragemen

t to

one

Labo£atorx

The laboratory approaches the study of community stability and maturity through comparative
studies of the structural aspects of ecosystems. The assumption is made that changes in species
diversity within selected tropaic levels will reflect decreases in stability and/or maturity due
to environmental insults whether natural or man caused.

One ecosystem studied was a local stream in the area of suspected source of pollution.
Random samples of benthic invertebrates were collected and catagorized at several locations
above and below the suspected pollution source, similar collections were made to compare old
fields at different stages of laturity and to measure the extent of injury to a forest which has
bean selectively logged.

From the collected data spacies diversity (D) [ 4 ] values were computed based on the Shannon-
weaver function from the field of information theory

D = "I Pi l°g2 Pi

where is the fraction of the total nuaber of species belonging to the i th species.

The use of
responsible for
the tedious cal
◦f the studies
continually exa
sharp contrast
calculations w
Finally, the av
hypotheses tha
calculations.

automatic data processing as an integral part of the laboratory has been largely
the change of amphasis to quantitative studies of communities. The freedom from
culations required when large data collections are analyzed has widened the scope
now possible. Almost instant processing of collected data allows students to
mine the validity of hypotheses and to revise experiments in progress. This is in
to previous procedures where students collected great amounts of data before
ere made and frequently found froa the calculations that the data was worthless,
ailability of programs for statistical analysis has encouraged students to test
t previously could not have been considered because of the time required for

ERIC

MODEL OF A SIMPLE ECOSYSTEM

PLANTS HERBIVORERS CARNIVORES

A s

2253.

, B =

966.

C a

97.

TIME.

A s

2024 .

8 =

890.

C a

92.

time

A =

1901 .

B =

782.

C a

87.

time

A =

1787 .

B =

659.

C a

85.

TIME

A =

1734.

B a

545.

C a

85.

time

A =

1724.

B a

508.

C a

80.

TIME

A a

1726.

8 =

527.

C =

76.

T IMF

A a

1674.

B a

522.

C a

72.

TIME

A a

1658.

B a

463.

C a

75.

time

A 5

1665.

B s

384 .

C a

74.

TIME

iou

A =

1689.

B =

319.

C a

71.

TIME

A a

1736.

B 5

260.

C a

74,

TIME

120

A =

1621.

B a

228.

C a

76.

TIME

130

A =

1911.

B a

230.

C a

78,

TIME

140

A a

1979.

B a

216.

C a

75.

time

150

A a

2062.

B a

230.

C a

67.

time

160

It-

A =

2185.

O a

235.

C a

68 .

time

170

A =

2277.

B =

262.

C a

72.

TIME

180

A =

2359 .

B a

285.

C a

73.

TIME

190

A =

2423.

B a

328.

C a

71.

TIME

200

U_.

A a

2443.

B a

377 .

C =

73.

TIME

..ZX.^. .......

A =

2430.

B a

493.

C a

70.

TIME

220

A a

2432.

B a

595.

C a

72.

time

. 230 _

A =

2314.

B =

665.

C a

75.

time

240

A r

2194.

B =

682.

C a

74.

time

250

A a

2086.

B a

675.

C a

75.

time

260

A a

1988.

B a

686.

C a

71.

TIME

270

A =

1908.

8 =

614.

C a

68.

TIME

280

A a

m 1854 .

B a

606.

C a

6e.

.TIME

^ 9Q

A a

1 790.

0 =

571.

C a

68.

TIME

300

A a

1731.

B a

555.

C a

66.

TIME

310

A =

1665.

B =

533.

C a

70.

TIME

320

A .

1661.

B a

477,.

C a

7.1 j.

.TIME.

.J53Q

A =

1653.

B a

412.

C a

71.

TIME

340

A a

1651.

9 =

365.

C a

... 72.

-TIME

z _

.. 350

A =

1700 .

B a

281.

C a

72.

TIME

360

A =

1766.

B =

250.

C a

73.

TIME

370

A a

182i.

B a

214.

C =

68.

time

380

A s

1937.

B a

215.

C a

64.

time

390

A a

2034.

B =

221.

C a

61.

time

400

A =

2112.

B =

230.

C =

62.

.time

410.

A =

2189.

B a

252.

C a

63.

TIME

420

v ,

A s

2236.

6 a

294.

C =

69.

TIME

430

A =

230 U .

B a

348.

C a

72.

TIME

440

A =

2344.

B a

428.

C =

67.

time

450

"‘"As''

2306.

0 ~ a

‘56 lT

C a "

64 .

TIME

460

A =

2241.

S =

632.

C a

67.

time

470

A a '

2122.

B a

678.

C a

66,

T IME

460

2027.

B =

694*.

C a

64,

TIME

490

A -

' 1952.

B a “ ’

665.'

“67;

' T i"E

500

TABLE 1

^onci us^on

The authors have interpreted the following observations as to sean that coanuter support of
the undergraduate ecology course has been a success:

1. laproveaent in test perforaaace in areas relating to population dynaaics
2m k draaatic increase in the nuaber of students electing independent study in ecology

3. Coaputer job log records that indicate that a significant nuaber of students did

aore than the ainiaua required aaount of gaaing
4* Student interest in lab has increased

5. The aaount and quality of student data and the interpretation thereof has iaproved
greatl y

6. The student aorale in lab is noticeably better

da are pleased with the present and planning aore extensive coaputer use in the ecology course
in the future.

R EP8BENCES

1. Snith , J, N. , I960, IiSi§ IS £121231# Caabridge.

2. Cause, G. F-, 1932. "Eco.lngy of populations," Quart. Review Biol,, 7:27-46.

3* Spain, J. D,, 1970, Soae roaputer ££ogta§§ fi2£ £l2l23l2ll §L£i232£§* Bich, Tech. Univ.

4. Shannon, E. E., and Reaver, H. , 1963. Tfcg flatfceaatiSal 1£§2 £1 2t £2Mtai££ti2fi- University
of Illinois Press, Urbana.

7 fit

Problem:

Develop a graphic using

CONTINUUM by Edwin Young
functions, departing from the steriotyped final

presentation

QUANTITATIVE ECOLOGY FOB UIDERGBADOATES

Stephen R. Kessell
Aaherst College
Aaherst, Massachusetts 01002
Telephone: (U3) 542-3125

The past decade has seen a draaatic shift in ecology tovards detailed quantitative
techniques, systeas analysis and the aatheaatical aodeling of biotic-abiotic interactions* The
holistic approaches of the International Biological Program, the Hubbard Brook Experiaeatal
Forest, H. T. Odua's (1971) analog aodels and Margalefas (1960) applications of cybernetics to
ecology have becoae faailiar to undergraduates early in their training* A nuaber of texts
popular at the undergraduate level, including Eugene Oduaas (1971) fundamentals of Ecology, 8*
B. Ford's (1971), Ecological Genetics and several titles in the "Current Concepts in Biology"
series (especially Whittakeras (1970) Coaaunities and Bcosvsteas and Boughey#s (1960) Ecology oj
Populations) are stressing quantitative techniques~and aethods o. aodeling and siaulation* Yet
aany undergraduates - including advanced students conducting serious research - lack the
background to critically evaluate these ideas and to incorporate aatheaatical approaches iato
their ova work* This paper: will discuss our tvo years1 experiences atteapting to alleviate this
problea by teaching quantitative ecology at the level of the introductory ecology course at
Aaherst College*

Ecolpqy at Aaherst

Aaherst is a saall, highly selective aenas college firaly devoted to the liberal arts
traditions; its student body is outstanding and highly aotivated* Within the liberal arts
framework, the student has considerable flexibility in constructing his ovn prograa, allowing a
fairly high degree of specialization in aany cases* Although no "ecology11 or "environsental
science" aajor is offered, usually from 2 to 5 graduating seniors annually eoter graduate school
in ecology* Three alternative aajors are offered to such students: (1) the regular biology aajor
with specialization and research iu ecology and population biology, (2) an interdisciplinary
"natural sciences" aajor including work in biology and tvo other fields (usually cheaistry,
geology or aatheaatics) , and (3) a prograa of "Independent Study," under which all college
requireaents are waived and the student conducts course work, independent reading and research
under the direction of a tutor* Excluding the senior honors seainars in ecology, three formal
courses are offered in the field: Biology 41, Ecology; Biology 26, Diversity in Biological
Systeas; and Biology 40, Aquatic Ecosysteas* As all potential ecologists are introduced to the
field through the first course, it seeaed the best vehicle to introduce quantitative techniques*

Described as "a study of the relationships of plants and aniaals (including Ban) to each
other and to the total environment , " Biology 41 is an elective for sophoaores with a
prerequisite of genetics; this is occasionally waived for yell-prepared or highly aotivated
students* It is taught by Professor Lincoln Brower, and I take this opportunity to thank hia for
his coaplete and extensive cooperation and enco urageaent in aodifying the laboratory portion of
his course; I also thank Elizabeth Steele, Acadeaic Coordinator of the Aaherst College Coaputer
Center, for her extensive help and cooperation* Scheduled for three hours of lecture and tvo to
five hours of laboratory/f ield work a week. Biology 41 often requires extra outside lab work,
and deaands competent and well-written lab reports* As it was decided that new aaterial could
not be added to the course that necessitated sacrificing aaterial currently included in it, all
changes were aade in the laboratory portion of the course*

Computer Facilities

A variety of computational facilities are available to Amherst students* The biology
laboratories are equipped with four Wang 360 desk calculators; students have access to several
programmable calculators, including a Wang 700 with typewriter output* Four terminals provide
APL/360* The acadeaic computer center houses a two-disk, 16K IBB 1130, with high speed reader,
line printer and plotter* Although no coaputer science courses are offered, six non-credit
FORTRAN lectures are given each semester, while advanced FORTRAN and APL instruction is
available on a tutorial basis* No fees of any kind are charged to students for coaputer use*

Teaching Quantitative Ecolog ys Preface

For a nuaber of reasons with which my colleagues may disagree, we feel that the 1 130 is our
best available tool for teaching programming and aatheaatical techniques* Although using APL or
the der.k computers allows a student to concentrate all of his efforts Oti tt*e prograa at hand,
there is an aura of the "magic box" and a frequent feeling that tne machine is aoing something
mysterious and incomprehensible - something that only "experts" understand* As the student will

certainly be laced vith a real systea in the near future, we chose to begin with a saall systea
the 1130 - and teach the rudiaents of the aonitor and disk operating systea while we teach

FORTRAN and statistics. The results support our choice,

A number of problems confront any effort to teach quantitative techniques within the
fraaeworfc of an existing course. The majority of the students have never used a coaputer
systea or programing language, although perhaps half of the class has had soae experience with
electronic desk calculators. Their level of proficiency in aatheaatics includes a seaester of
calculus at best, and virtually none of the students have any background in statistics. A
consideration of the work- load is of paraaount iaportance; it is not possible to aerge an
ecology course and an introductory statistics/prograaaing course and expect the student to
double his conaitaent for single course credit. If we are not to delete a&terial troa an
existing course, we aust balance the new aaterial to be added against the extra work and tiae it
deaands troa the students; the single solution in reducing this load is to teach both ecology
and aatheaatics at the sane tiae. The success in carrying out this strategy will in large part
determine the success of the course.

Below is a week by week synopsis of the course's laboratory, in which we shall try to
evaluate the good and bad points, the successes and the failures.

Phase 1

Biology 41 originally included 10 laboratory exercises; although aost have been
considerably rewritten, they have all been retained, and serve as the core of our quantitative
laboratory.

The student starts using mathematics in the first laboratory. It is a field trip to study
light relations in a forest community, and the role of light and abiotic agents as limiting
factors. Overlooking the Connecticut River, students compare the forests and underjtory
vegetation of the flood plain to the lower slopes of the Holyoke Range, and in a successional
comaunity of eastern hemlocks (Tsuga canadensis) measure distanczs between an individual tree
and its nearest neighbor and the aean diameter of the two trees for 100 such pairs of trees. In
the report, they are asked to discuss the role of light as a limiting factor in the community
based on their own findings and studies in the current literature (Ovington, 1962), A scatter
diagram and least squares fit is required, and while doing the fit by hand, it becomes apparent
that there must exist an easier way to conduct the repetitive calculations. "Maybe the
computer. . • "

The second lab is the qualitative construction of a food web for a saall pond coaaunity
based on samples collected in the field. While they are writing up the report, we begin teaching
quantitative ecology in earnest.

The opening lecture on programming is given in the regular lecture tiae period (and is the
only formal class time sacrificed). It covers a general introduction to the coaputer as a systea
- what it is and how it works. Although a number of points are obviously oversimplified, the
student learns what a program is, what it means to compile and store a program, what the core
storage and disk are, why a user must aake certain specifications to the machine, why a
programming language understandable to both machine and user is necessary. •• in short, he has a
vague idea of what happens when he pushes the program start button. Pinally, the fora and
format of a FORTRAN program is roughly covered, including the distinction aaong arithmetic,
specification and control statements. A three hour session is scheduled tor the following
evening. Attendance is not required, but next week's laboratory will require a user-written
program to solve a portion of the problem; the report is unacceptable without it.

Perfect attendance... During the first session, each student received the Coaputer Center's
booklet on FORTRAN programming and the 1130 systea as a re terence/study guide, and the current
Newsletter discussing operating procedures (ours is a hands-on systea) , descriptions and
documentation of our general purpose subroutines, special packages and disks available, and the
like. These materials are designed to coapleaent the class work, and to serve as readable
references (unlike some of the foraal user guides) • We now pound FORTRAN for two hours.

We start with the control cards and why they are used. We next review arithmetic statements
and simple control statements (IF and GO TO); next come READ and WRITE statements. This leads to
the use of FORMAT statenents (I and F only at this stage) . we do* not cover vectors and arrays
until the next session - after DO loops. In about an hour, we have the basics to allow us to
write siaple programs.

We have found this to be our best tool - siaple programs relevant to the course's lectures
and labs. With their notes before them, we pose siaple biological problems and write FORTRAN
program solutions on the board. We begin with very simple problems (see Figure 1) and involve

ERsLC

1 1

i w i *

the whole class (of 15 students) in the solution* The response is slow at first, and then picks
up. rfe are certainly aided by the class9 saall size (which is split into two lab groups), our
familiarity with the students and their background, and the use of relevant aatenal froi the
course. Neai: the end o£ the session, we tackle the least squares fit froi the first lab and
write a prograa (using one of the available subroutines) that is five stateaents long and will
require five minutes to funch and run. When we look at the output and grapn, aost students are
thinking of their tour hours of tediua and are convinced that the task of learning FORTRAN just
might be worth it.

By the end of two hours, everyone has handled cards and output, so we head for the coaputer
center. Within an hour, everyone has learned to use the keypunches and run a program. The third
- and last - formal session is scheduled.

The last group meeting continues the writing of simple programs, and introduces the DO
loop; through these programs, we meet the need for vectors, arrays, E formats, computed GO TO*s,
and pauses. We end on the vegetation distribution problem shown in Figure 2, and no one has any
real difficulty in writing the FORTRAN prograa. This program is very similar to the one required
in the next lab exercise.

Lab 3 is a st dy of succession and indicator plants along a transect of a peat bog. The
Horizontal sequence of species in space coapares to the vertical sequence in tiae; six indicator
plant species are counted in seven plots extending froa the pond edge to the black spruce fpicea
Eiriana) forest. In writing up the report, we make a trade-off; the instructions call for a bar
graph or frequencies witnin the seven plots. This is written for the students and stored or the
class* disk; only an XEQ and 7 date cards are required to produce the graph. In exchange, each
student is required to solve fo> the centers of distribution using his own prograa. A slight
curve is thrown - the plots are of unequal sizes, so the center coordinates aust be read in as a
vector. The author, who serves as laboratory instructor in the course, is available four
evenings that week at the coaputer center. By the tiae the lab is due the following week,
everyone has his program and results. Each student has taken his own problem and field data,
written a successful program and produced the needed answers. "It works. ..»» We are now over the
hump.

The time required ot students and instructor alike is obvious. But a week earlier aany of
these students had never seen a computer. We (including the students) think it was worth it. The
next two labs require no written report and provide both a breather and an or- ctunity to
experiment with the computer. The author is available at the computer center iu: evenings,
while the center personnel are available full-tiae to assist and teach programaing.

Although these two no-report labs are of no mathematical interest, we include a brief
description for continuity. Lab 4 is a one hour flight around the Connecticut River valley,
taking the pilot, professor and four students at a tiae. We look at areas already studied, areas
about to be studied, the dynamics of a large river system, the geology of the Holyoke Range and
the beauty of nature exemplified by New England autumn foliage. Lab 5 follows the same route
frofli the ground - the Connecticut River as a system. We stomp around the flood plain, old
channels, oxbows, meanders and successional forests. After all, mathematics i*; only a tool for
handling this fantastic system.

Phase 2

Lab 6 is formally called ''Modeling of the physical factors limiting eastern healock growth
in Pelham, Massachusetts": in one year, it has become known as "The Healock Lab" and has earned
a certain degree of infamy. To briefly describe the background, eastern healock (studied in Lab
1) uas an unusual bimodal distribution in southern New England (Kessell and Brower, in press).
It is found in the fiats and ravines of saall streams and on the upper slopes of the lower
mouutains (below about 2500 feet HSL) , but is uncommon on the intervening slopes. In the first
lab, we concluded that sunlight and "other factors" limited growth; the students are now asked
to not only determine what these factors are, but to quantify their effects as well, and to
produce a mathematical model allowing the prediction of annual growth rates froa env ironaental
data alone. Furthermore, they are asked to both qualitatively and quantitatively explain the
species' bimodal distribution and the environmental and/or genetic basis for it. They have five
weeks in which to complete the lab and write it up.

A field trip to the area under study - two stands, one on an exposed hilltop and one at the
stream flats at the base of the hill - shows the students tuc basic differences in flora and the
abiotic environment at these extremes where healock predominates. But on the intervening slope,
under conditions intermediate to those found where the species thrives, hemlock is below the 1%
level. Cores are taken from ten individuals at the two stands with an increment borer, and
students measure annual rings for 40 years for each tree. They are provided with the general
curve of growth rates as a function of ?ge (Pigure 3), an equation offering a possible
approximation of this function, monthly cliaati data for eight variables tor the 40 year

23 ,2

Figure 3

Typical growth curve of an Individual eastern hemlock

Tha solid h na. a tha actual anm>al r*g width.

T ha daahad hna •• an appronmation ot th* tunctior ralating growth rata to
aga which may ba wnttan aa

V - a ♦ bX * cK2
whara V ia growth rata and X ia aga

Thi a aquat.on aaaumas a constant anvironmant

Tha abrupt changa to linaanty occurs whan tha traa raachaa canopy atatun

Tha actual growth curia (solid hna) >• cbtamad by adding amoronmantal
mdicaa* F0 and Ft> which vary from yaar to yaar. to tha a born
aquation, gnmg

V - a • bX Fq ♦ c X*F,

(attar brisking through tha canopy. Fj - 0 and tha aga Junction ia
tinaar )

F0 ia utad aa tha dapandant vtnabla in nx>tt ipla rtgraaaiona at growth on
climate. tha higher tha correlation. tha ctoaar tha modal appvonmatea
tha actual growth curva

Correlations with R- 0 ara common ( aaa tail)

Growth rates - moisture correlations of Tsuge canadensis
Ftolham, Massachusetts

Mean growth ratda and correlation* to mo.atura ravaal a phynoiog-cai d.morph.am
all individuals from tt» hilltop and aoma hemlock* tram tha van«y ara
tha low growth, low moatur* typb (caMbd Typa 2). Soma va'lay

Iwnlocli ara tha high growth rat*, high montura morph ( Typa I)

hemlock distribution in southern New England

Tha d<morphiam •■plan* tha spec** unusual d»alribu*K>n.

Ugh growth Typa 1 trait -imittd to ma*< a I tat. ah»la dnn^h

to** ran t Typa 2 hamlocha aa pradominant at mo»a itnc sdbb.

Aopartnfi, nttlhgr morph is a good compatitor under intermediate

condition! . Fm f# >s ticiudtd by tha pines and hardwoods an
th« mtarvamng awi-met* atopaa

period, a multiple regression prograa and our best wishes. The author aovos to the computer
center to offer suggestions, aid and contort.

It aust be pointed out that the current literature does not answer the questions raised ia
the lab. A nuaber ot studies of cliaatic control ot heal'ock growth and distribution (including
Avery £tt 1940; Baun, 1950; Olson e t, al, , 1959; Adaas and Loucks, 197H) are furnished to
the students7 but these findings are soaewhat inconclusive and occasionally contradict one an*
other. Studies of both the distribution of hemlock along eav ironaental gradients (Mhittaker,
1956) and seedling growth under controlled conditions (Olsoa ila.# !>•<:•) suggest ecotypes of
the species, but still do not explain the situation the students observe. The student soon
realizes that either he is to repeat these earlier attempts, or to find something new not yet ia
the literature.

Of course, the latter is the case; this problem has been investigated by tho author for the
past two years, and the lab very closely follows ay work - with all the frustration, excitement
and dead-ends coaaon to any research problem. And soaehow the students btcoae as excited and
involved as we are.

A little thought and tiae i
Schaua's Outline in Statistics to be
growing season climate aeans (using
is a good place to begin. But the cor
1 • c. , tound). Either climate is not
the growing season means are not adeq
1966; Kesseli and Brower, l.c.);
month througnout the growing season,
data - a 12-factor regression is com
T lie majority of the multiple H*s are
changes in climatic effects for each
output.

n the literature and statistical references (we*ve found
excellent) snows the students that regressions ot growth on
the Fq coaponent as the dependent variable [see Figure 3))
relations are not significant at P 3 .05 (as Avery et . nl. ,
a signficant factor controlling the annual growth rates, or
uate. It turns out that the latter is the cause (Fritts,
the effects of a factor differ significantly froa aontb to
The regressions are now repeated using individual monthly
pleted for each site and each of the eight cliaate factors,
highly significant, and the partial r's reveal the monthly
factor. The student is now the proud owner of 3U5 pages of

A week or so with t
valley to dry hilltop is
correlations to wind
correlations at the nill
correlations are direct
the temperature is above
and inverse correlation
limiting factor. This de
than moisture is limi
an d more limiting as the
correlations to moisture
Tne original hypothesis
limiting by moisture is

he data gives the basic picture. The environae ntal
shown in a nuaber ot ways, including the
noted at the more exposed site. Temperature
top site, but an optimum temperature of about 10*13
during months when the temperature is below this ra
it. In suaaary, at the hilltop site, direct corre
s to sunlight during the early spring suggest noist
pendence increases into the suaaer. At the valley
ting during the ground saturation of early spring;
suaaer progresses. A neat package, with one
are higher at the wet valley site than at the lore
that the lower growth rates on the hilltop are
rejected. An alternative explanation is necessary.

gradient froa the wet
nuch higher inverse
not only gives higher
degrees c. is noted;
age, and inverse when
lations to aoisture
ure to be the primary
site, light rather
aoisture becomes more
very bad flaw; the
xeric hilltop stand,
due to ao^e severe

t this point, the students have us3d only the aean growth rates of t
sample! at each site; they are now provided with the individual growth ra
correlations for every tree. We suggest that they plot aean growth rates
aoisture (expressed as the product of significances P) for the critical Hay-
resulting graph (figure 3) shows the responses clustered into two group
sampled at the hilltop and some individuals froa the valley exhibit low growt
correlations to aoisture, while the remaining individuals froa the valley e
rates and high correlations to moisture. The differences are highly signitican
both types are sympatric in the valley. Apparently we9ve found a dimorphism
morphs physiologically adapted to two different habitats. A aodel built on
(with the species excluded on the intervening slope by coapetiti vely better
hardwoods) will account for the species9 unusual distribution. He also have au
equations (with R = .9) giving a aean error of prediction of annual growth
5%.

he ten individuals
tes and aoisture
vs correlation to
July period. The

s. All individuals
h rates and low
xhibit high growth

t. Ecotypes?.. • Mo
- two specialized

these two aorphs
-adapted pines and
ltiple regression
rates of less than

The lab is a long one, b
their work, and hardly gripe ab
difficult problem - one in
answered a difficult question -
are handed in, we discuss (w
problem, including morphologica
gradient distribution of the
in press) • There are no readily
students have gone as far as
had never seen a FORTRAN progra

ut at its completion the stud
out the 20 to 30 page laj
which the mathematics alone
one wuich had no answers in
ith those students who are st
1 differences, sub-specific
two aorphs and their roles in
available answers to the!
anyone has, know it, mod are

ents show an innense satisfaction in
reports. They were given a very
would take years by hand. They have
the literature. After the reports
ill interested) other aspects of the
hybridization between the norphs,
interspecific competition (Kesseli,
r questions; at this point, the
excited by it. Eight weeks ago they

. < >

For the rest of the course, no sore prodding is needed. The students are* familiar with the
tools and basic statistics and use thea as needed. Rany are now using APL (at least as a desk
calculator) for small jobs, while the desk calculators have becoae "old hat." The following two
labs detemine population size, age structure and survivorship curves of sunfish in a saall
pond; the place of and need for computing tools and methods is obvious. They're on their own,
and really don't need our help.

The final twu labs study density-dependent survivorship a^u interspecific competition in
Drosophila. Although it is an excellent opportunity to introduce some new computing tools and
procedures, time does net permit too auch sophistication. The Wang 700 is moved to the lab tor
2-way A NO V A 1 s of competing species, and IBR#s analog simulator for the 1130 (C.S.R.P.) is made
available. So i±> a little Edmund Scientific analog computer to show basic analog principles.
From their data, a variety of methods (each involving different assumption ) for determining
saturation densities (K) and alpha and beta coefficients of competition are used, and ve all
argue about the validity of the assumptions.

ft strikes ae that we've come a long way in ten weeks.

In Retrospect

Perhaps a third of these students will go on in the field to become professionals. To the
nonspecialist, we hope to have given both an appreciation of the field and some understanding of
current research being carried out. To the future ecologist, we have tried to give a little
firmer foothold than he normally would have received. He is not only aware of the tools and
materials available, but is eager to incorporate them into his thinking and future work; he is
also eager to point our flaws in the thinking of others, including the autnof's. A small measure
of our success has become visible in the students' mathematical sophistication in later courses
and independent work. Although obvious time limitations preclude the addition of other
interesting material to this couLse, advanced independent reading and research courses are
becoming more common, within an interterm project, we are now incorporating the tree climate-
growth models into two-axis gradient nomograms (following Whittaker, 1967) using IBR's Numeric
Surface Techniques package to solve the orthogonal polynomials, and are attempting discriminant
analysis of the major components forming the niche hyper-space of Hutchinson (1966) and
Whittaker (1967, 1970). At this moment, three sophomores from the 1972 course are using this
technique to determine the differential responses of tour pine species growing in the same
community. Recognizing my own prejudice, these students may well have a three year jump on their
contemporaries.

Of course, not all we have done is fun and exciting. We have placed a considerable burden
of /ork on the students. Those truly excited by the field (and not only those with a
professional interest) will take the challenge. Those with a less ec interest may feel
overwhelmed or inundated with work, and it is critical that the instructors te prepared to
recognize this situation and offer help and encouragement when necessary. The distinction
between the student having problems he can best work out for himself and the student about to
give up is noi always obvious. We have to recognize that not all students in our course are on
their way to a doctorate in biology, nor are all we excited by the subject matter as we are.

A final word: the instructors of such a course must be prepared for a huge work load. Even
with only 15 students, three of us were kept on the go for the entire semester. Ptol^tsor Brower
taught his course, the author taught the quantitative techniques and programming in the
laboratory and computer center, and the computer center people kept the center running smoothly.
We think it was worth it.

REFERENCES

Adams, tl. S. and 0. L. Loucks. 1971. Summer air temperatures as a factor affecting net
photosynthesis and distribution of eastern hemlock (Tsu^qa canadensis L. (Carriere)) in
southern Wisconsin. Am. Midland Naturalist 85: 1-10.

Avery, G. S., H. B. Creighton and C. W. Hock, 1940. Annual rings in hemlocks and their relation
to environmental factors. Am. Journal of Botany 27: 825-831.

Bouqncy, A. S. 1968. Ecology of Po Pulations. New York: Hacmillan. 135 pp.

Bran;, E. L. 1950. Deciduous Forests of Eastern North America. Philadelphia: Blakiston. 596 pp.

Ford, E. U. 1971. Ecological Genetics , 3rd edition. London: Chapman and Hall. 410 pp.

Fritzs, h. C. 1966. Growth rings in trees: their correlation with climate. Science 154: 973-979,

Hutchinson, G. E. 1965. 7^e Ecological Theater and the Evolutionary Play, Vow Haven: Tale
University Press. 139 pp.

Kessell , s. R. Ecotypic polyaorphisa in the eastern hemlock* Tsuqa canadensis, Submitted to The
American Naturalist.

Kessell, s. B. a^d 1. P. Brower , in press. Siaulation of the effects of cliaatic limiting
factors. I. Niche variation in the eastern t^mlock, Tsuga canadensis. Ecology.

Margalef, R. 1 96 d. Perspectives jn geological Theory. Chicago: University of Chicago Press. 113

pp.

Oduc, K. p. 1971. Fundaaentals of Ecology, 3rd edition. Philadelphia: Saunders. 574 pp.

Odum, H. T. 1971. Environment, Power and Socket*. New Tork: Wiley. 331 pp.

Olson, J. S. . F. w. Stearns and H. Nienstaedt. 1959. Eastern henlock growth c^jles and early
years. Conn. Agr. Exp. Station Circular No. 205.

Ovington, J. D. 1962. Quantitative ecology and the woodland ecosystem concept, ig j. B. Cragg
^ed.) Advances in Ecological Research, Vol. 1, ''p. 103- 192. New York: Academic Press.

Spiegel, M. H.
NcGraw Hill.

Whittaker, R, H.

Whittaker, R. H.

1961

359

1956.

1967.

1970.

Theo £1 and Problems o£ Sta tistics (Schaun*s outline Series).

pp.

Vegetation of the Great Smoky Hountains. Ecol. Nonog. 26: 1-B0.
Gradi, .t analysis of vegetation. Biol. Rev. 42: 207-264.
Coaaunities and Ecosystems. New York: Nacaillan. 162 pp.

New York:

DIGITAL AND ANALOG COflPUTING IN GENERAL ANIMAL PHYSIOL OGY

Howard C. Howland
Cornell University
Ithaca, New York 14850
Telephone: (607) 256-4716

ABSTRACT

Laboratory anl hoaework exercises in analog and digital computing have been introduced into
an upper undergraduate course in general animal physiology in order to increase the amount and
depth of presentation of quantitative material. The analog coaputer was chosen initially for its
physical similarity to aatheaatical flow diagrams of physiological control systems.
Subsequently, a saall digital .coaputer was added and used both for numerical simulations of
control systems and for solution of booework problens requiring only elementary prograaaing
skills. A critical factor in the response of students to these innovations appears to be their
prior exposure to applied mathematics in the sciences.

Introduction

General aniaal physiology is a field rich in quantitative topics which deserve, but do not
always receive, serious treataent in undergraduate courses. Phenomena surrounding the
transmission of the nerve iapulse, osmosis, auscle dynaaics, enzyae kinetics, countercurrent
exchange* and, nost generally, homeostatic feedback control systems all require a quantitative
presentation if the serious student is to understand themll].

The aathematical background required for a treataent of these topics is primarily algebra,
of which our students generally have adequate command, and differential equations, a knowledge
of which our students are usually innocent.

Since a majority of biology students lack a formal background in differential equations,
and since the great majority of physiological feedback systems studied contain important non-
linearities rendering them relatively intractable to formal solution, it seeaed reasonable to
turn to the teaching of analog and numerical techniques for obtaining specific solutions of
given feedback systems.

In all candor, 1 am not now sure that it is possible to do this successfully entirely
within the bounds of a physiology course. But one fact was certain when this endeavor began;
naaely, the problem of providing an adequate aathematical background was not being solved
elsewhere in our curriculum.

MATHEMATICAL PLOW DIAGRAMS AND ANALOG COMPUTING

A Flow Diagram Notation

It has probably occurred to many persons that analog computer flow diagrams are almost
machine independent, and that they are essentially mathematical structures.

This struck me at a moment when 1 was particularly vexed with the ambiguous "arrow"
diagrams common in physiology. I mean diagrams which proport to say something about the dynaaics
of feedback loops (often labeled with "EXCITATION" and "INHIBITION") but which, in fact, are the
mere mental props of their authors, with little meaning for others.

In any event, I sought to replace these with something specific, and I chose a notation
similar to that used in analog computing with a few minor changes in convention (Figure 1) £ 2 J.
Several lectures were used to introduce this notation to the students and it was then employed
to describe models of physioloqical feedback loops. (Figure 2.)

One curious fact emerged immediately from my students1 attempts to understand these
diagrams. On the one hand, the diagrams had an intuitive appeal quite apart from their
aatheaatical precision, as demonstrated by students9 ability on tests to answer correctly
questions concerning the implications of a diagram, without being able to write the equation
system that the diagram represented!

,? 28

Figure 1.

Operation

A constant

FLOW DIAGRAM ELEMENTS
Symbol

Function

(k) — X

X = k

Multiplication
by a constant

X = kA

Addition

a — rv_
!=l>~

X = A + B + C

Subtraction

A —
B —

X = B - A

Integration

X = Y

+ C (A+B-C) dt

Multiplication

X = A • B

Division

X = A/B

Comparison

X = +1 if A > B
X = 0 if A 5 B

"Proportional

Comparison"

X = A-B if A-B > 0

X = 0 if A-B < 0

Figure 2 Flow diagram eleaents. The aajor difference between this notation and sore
conventional analog coaputer notation is the representation of inversion, here a dot at the
input. Mote that the denominator input in a division operation is denoted by placing it belgw
the nunerator input.

ERIC

<*18

2»

Figure 2 A flow diagram for a simple model of temperature regulation. Metabolic heat, M, is
"produced" vliea the body teaperature, TV falls below a set-point, Tg. Heat is generated in
proportion to the difference between the set-point teaperature Ts and the actual body
teaperature. Heat is lost froa or gained by the body at a rate, X, which is proportional to the
difference between the environaenta 1 teaperature, Te, and the body teaperature T^. The

differential equation for the systen is:

On the other hand, a single, elenentary point continually led students astray. Por a long
tine aany students insisted upon seeing the lines of the diagraas as paths through which fluids,
horaones, nerve iapulses, what have you, - flowed. It was often a hard fight to convince then
that the line siaply represented a particular variable in the systea which could assune a value
which night or night not change with tine, depending upon the systea. (Appeals to their
intuition to interpret the lines like voltages or p;;essures were futile.)

A second pedagogical difficulty arose when I discovered that there was perhaps good reason
for the old, iaprecise diagraas of the physiology cexts--nanely , aany of the systeas which are
considered very well understood are, in fact, understood in no dynanic, quantitative way at all.
This, of course, is exactly the virtue of a aa thenatical flow diagran, in that it forces one to
record in a systeaatic way all of the dynaaic infornation that he possesses about a systea.
However, when one is considering a ’classical" physiological feedback systea in an undergraduate
course, and the quantitative infornation about it turns out to be precious little, one aay well
wonder at the wisdoa of such a treataent.

The ft'cts are, that while the dynaaics of soae physiological systeas are well understood.
Others are not, and the physiologist is well advised to choose his exaaples carefully.

Using the Analog Coaputer for fcgfiture Deaonsty ations

Perhaps the aost effective use of the analog coaputer is in lecture deaonstrations. This is
because a large nuaber of students can watch the output of the coaputer siaultaneously and the
coaputer can be aanipulated by one who is skilled in its operation.

A typical use of the coaputer in this aode would be to deaonstrate a aodel of the feedback
loops involved in the generation of the vertebrate respiratory rhythn. (Figure 3.) The systea is
of particular interest because one can siaulate sectioning parts of the real physiological
systea by perforaing the corresponding "operations" on the aodel systea, and show that the
behavior of the systea is analogous to that of thu aniaal.

dQ/dt = k,Z ♦ k3(k2Q-Te)
where Z = Ts-k2Q for Ts>k2Q, else Z = 0.

Thermoregulation Model

Body

Q temperature

Heat loss

* — Environmental
temperature

Figure 3.

Respiratory Rhythm Model

Pneumotaxic

Center

Apneusiic

Center

Medullary

Center

Lungs

£iaat§ 2 A aodgl of sespiratorjr r^ythj generation. The node! consists of various
qualitative aspects of respiratory rhytha physiology can be demonstrated on the model such as:
(a) showinq that the rhythn will persist in absence of vagus inhibition but that the respiration
will be deeper and slower; (b) persistence of the rhythn in the absence of feedback froa the
pneunotaxic center in the pons but not without vagus feedback; (c) persistence of the rhythn
without the pneunotaxic center and the apneustic center. The nodel is based on a sunaarv of
facts presented in Comroe (1965)* 1

ERIC

A virtue of the analog computer over the digital coaputer at the current state of the art
should be aentioned here- naaely, it provides an econoaic aeans for siaulating in rea 1 tiae
relatively rapid physiological processes which would tax any digital aodel written in a higher
level langauqe.

AUiioa Computing in the Laboratory

After using the analog coaputer in lecture deaonstrations we were anxious to allow our
students in the laboratory portion of the course to have an opportunity to obtain solutions to a
siaple equation systea on it. Since our laboratory students already have had soae faailiacity
with polygraphs and other electronic equipment it is possible to give then a rough idea about
the principles cn which the analog coaputer works without their having had an extensive
background in electronics.

This year we hope to supplenent this background by introducing thea to the use of
operational aaplifiers as part of the signal processing of physiological data. He hare
constructed batteries of ten operational aaplifiers in a convenient plug-board arrangeaent for
this purpose (Figure 4).

In our computing exercises we have students obtain specific solution to a thermoregulatory
control loop and to a long tern problea in weight regulation which they can then compare to
solutions that they obtain on the digital coaputer (to be discussed below).

A major problea in the use of the analog coaputer in the laboratory is the liaited number
of students which can aeaningfully work at the coaputer at one tiae. The optinua nuaber would
appear to be two students at a tiae and certainly not aore than three. This requires a
considerable coaaitnent of laboratory and teaching assistant tiae, as well as a large equipaent
investaent [3] •

Piqu£e 4 Ajl operational manifold for signal processing i g, £he phvsi ologicai laboratory. The
aaaifold consists of 10 operational aaplifiers and a power supply (Models 105A and 902, Analog
Devices Inc.) He have arranged the feaale plugs in such a fashion that connections between
aaplifiers can be Bade with components mounted on standard bannana plugs with 3/4" spacing.
Bach aaplifier is provided with two negative input points, two output points, one positive input
point, three grounding points and a neutral point. Baking eight feaale bannana connectors in
all* The aanifold finds use in adding, subtracting, filtering, and integrating physiological
wave forms.

DIGITAL COB PUT IMG

Introduction

Instruction in digital confuting is undergoing a rapid change primarily due to the
introduction of aini coaputers into aany curricula. In our own course ve purchased a snail
digital coaputer in place of a aultiple capacitor delay unit for our analog coaputer. tfe rapidly
discovered that the digital coapater offered enoraous educational possibilities as a stand-alone
coaputer itself, in aany ways aore powerful than the (Bore expensive) analog coaputer.

Previously, our only access to digital coaputing had been through batch-processed languages
available to students only with very long turnaround tines. The aini coaputer afforded us
immediate turnaround and meaningful results in the laboratory via its interactive language,
FOCAL. Currently there are a wide variety of aini coaputers available, all of which offer
interactive FOCAL or BASIC, or both, and hence are suitable for the applications discussed
below.

"Stca iqht Li ne" Programming to Solve Quantitative Hoaeworh Problems

One of the first uses we put our coaputer to was to ease the coaputational load of our
students in solving quantitative hoaework problems. This was done by teaching then "straight
line" programming i.e. progranaing which involved no iteration or logical branches. A student
can learn these eleaentary aspects of prograaning within about a half an hour at an interactive
terainal. This aaount of computing knowledge greatly increases his or her coaputational
skillsf 4 ].

A typical "straight line" prograaning problea is given in Figure 5.

C-FOCAL, 1969

01.10 ASK ?R? , "PRESSURE IN MM HG ",?P?,!
01.20 ASK ?L,VI ?, !

01.30 SET PI=3. 14159
01.40 SET P = P*1333. 22
01.50 SET Q=PI*P*Rt4/(8*L*VI)

01.60 TYPE "FLOW IN CC/SEC" , %12.03, Q,!
*G0

R: .08 PRESSURE IN MM HG P:15
L, : 4 VI :.04

FLOW IN CC/SEC 2.011

Figure 5 — A "sinaight line" program in FOCAL (i^e^, a program with no logical branches 0£
iterative loops) . The prograa coaputes the flow of blood, Q, through a hypodermic needle whose
length and radius are specified. The pressure drop along the needle and the viscosity of blood
are given as input paraaeters. Use of such a prograa completely documents the procedures used in
the exercise. Readers unfaailiar with FOCAL aay translate the program into BASIC by substituting
LET for SET, INPUT for ASK and PRINT for TTPE. The program is taken froa Howland, (1971).

In learning to write such a prograa a student has:

a. obtained connand of certain functions (like eEE)
which he aay not have had before;

b. learned to foraulate the problea in sufficient generality
to solve any similar case with different input values;

c. and (assuaing the solution is correct) aade a legible record

of his oethod of solution which he can refer to any tiae in the
future or, (if the solution were incorrect) , aade a record of
his aethod which can easily be corrected in the future.

I believe that the combination of generality and documentation in such elementary
prograaaing shills puts our students veil ahead of even accomplished students who operate with
pencil, paper, and a slide rule. One great advantage of the digital computer is its enforced
documentation. This is an enormous boon to a teacher who must either wad© through piles of
scribbled homework, or take the answers on faith and abandon all hope of correcting his
students* mistakes[ 5 ]•

Numerical simulation o£ ph vs iol o q lea l_3*fl tens

With the introduction of a digital computer into the laboratory we began using it along
with the analog computer to simulate physiological systems.

To accomplish this we wrote a general purpose, second order Bunge^Kutta routine for solving
sets of first order differential eguations. The students were then reguired only to program the
differential eguations that the Hunge-Kutta routine would solve.

Figure 6 shows the listing ol the Runge-Kutta routine with eguation subroutine and typical
printout. It will be noted that the equation system we have simulated for this example is
identical to that given for the analog computer respiratory rhythm model in Pigure 3,

C- FOCAL, 1 969

01.05 E

01.10 T H* "ENTER RUN PARAMETERS"* ! !

01.15 A ?ND* IP* PN* TS* TQ ?* !

01.20 C PLACE INITIALIZATION STATEMENTS HERE

01.22 T !! "SET CONSTANTS"*!!

01.25 F J = 1 * 9 J T "K"* %3* J * " "• A KCJ>;T %5.03* K(J)*!

01.30 T !! "INITIALIZE INTEGRATOR'S'*!!

01.50 F J= 1 *NDl T % 3* J i A ?YCJ> ? !

32.23 S H=(TQ-TS)/CIP*PN)

02.2 4 S TM=TS

02.30 T !! " TIME Y C 1 > Y<2> YC3) PLOT OF YC2) "* ! !

02.31 D 3*35

02.32 F IT=1*PNJ D 3*00

02 • 40 T !!* %6 • 0 5* ?H ?*%4*" NO. )F INTERVALS "*IP*PNiO

03.33 F I = 1 * I P ; S TM = H*( ( IT- 1 ) * I P* I ) + TS * D 4.0

03.35 T %6.03*!*TM;F I=1*NDJT " "*Y(i>

03.36 D 6.0

04.12 F L=1*ND;S 0L(L)=Y(L)1S R<L)=0

04.13 F L=1*2;D 8 . 0 * D 9.0

04.14 F L=l*NDiS Y(L)=0L(L)+R(L)/2

06.10 F L=0*.1*Y<2); T " "

06.20 T "*"

08.05 C PLACE DE EQUATION SYSTEM HERE

08.10 S Z=C+K<2)+K< 3>-( K( 7 > ♦YC 1 )+K( 4>*Y(2>+K( 9 >*Y< 3) )

08. 1 5 S C=. 5*FSGN(Z )♦• 5

08.20 S DC 1 )=C*K( 6)-K< 1 )*Y( 1 )

08.30 S D(2) = C*K(8>-KC 5>*YC 2>

08. 40 S DC 3> = D< 1 >

09.11 F M= 1 * ND* S R(M)=H*DCM) + RCM)

09.20 I CL-D9.3JF M=1*ND?S Y C M ) = Y C M ) ♦ R C M )

09.30 R

figure £A — I second grdey Bunue-Kutta program for systems of first order differential equations.
The program is written in FOCAL, The eguations for the differential eguation system are in
section 0,0, in this case, the eguations are for the respiratory rhythm model of Pigure 3, The
program is sufficiently general that it can be adapted to any eguation system by minor changes
in statements 1,25 (setting the number of constants), and 2,3 (output titles) and 6,1 (plotter
parameters) •

ENTER RUN PARAMETERS

ND> 3 IP, 2 P N,20 TS> 0 TQ 20

SET CONSTANTS

K l .077 0.077

K 2 .2 0.200

K 3 -2 0.200

K 4.5 0.500

K 5 .2 0.200

K 6 .2 0.200

K 7 .5 0.500

K B .4 0.400

K 9 .5 0.500

INITIALIZE INTEGRATORS

1 Y( J)

2 Y ( J )

3 Y < J )

TIME

Y( 1 )

YC2)

Y( 3)

PLOT OP Y C 2 )

0.000

1 *000

0.193

0.362

0.193

2*000

0. 371

0. 658

0.371

3.000

0. 536

0.90 1

0.536

4 • 000

0. 688

1*100

0.688

5 . 000

0. 780

1.163

0. 780

6 • 000

0. 722

0.953

0. 722

7.000

0. 669

0. 780

0.669

8*000

0.619

0.639

0.619

9.000

0.573

0.523

0.573

10.000

0.531

0.429

0.531

1 1 .000

0.49 1

0.351

0.491

12.000

0. 455

0.288

0.455

13.000

0.421

0.236

0.421

14.000

0. 390

0.193

0.390

15.000

0.361

0. 158

0.361

16*000

0.384

0.229

0.384

1 7.000

0. 548

0.550

0.548

1 8 • 00.0

0.700

0.812

0 . 700

19.000

0.841

1 .027

0.841

20.000

0.825

0.923

0.825

H 0.50000 NO. OP INTERVALS 40*

^ ifidsi aiik ill ga£ts The lung volune r(2) is also plotted as
■ell as printed. The run paraneters are: HO = nunber of deriuatiTes, IP » nunber of points
coaputed betueen each printed point, PH = nunber of points printed, TS * starting tine. TO *
quitting tise, H is the step size in tine units. w

*G 1-22

SET CONSTANTS

1 0.077

2 0.200

3 L.200

4 0 0.000

5 0.200

6 0.200

7 0.500

8 0.400

9 0.500

INITIALIZE INTEGRATORS

1 YC J)

2YC J>

3YC J)

TIME

YC 1 )

Y ( 2 )

YC 3)

0 • 000

0.000

0 . 00 0

0 • 000

1 • 000

0. 193

0.362

0.193

2.000

0. 371

0.658

0.371

3.000

0.536

0.901

0.536

4 • 000

0.688

1.100

0. 688

5*000

0.830

1 .263

0.8 30

6.000

0.961

1 .396

0.961

7.000

1 .082

1 .506

1 .082

8-000

1.194

1 .595

1 • 194

9 . 000

1.298

1 .668

1 .298

1 0.000

1 . 395

1 • 728

1 .395

1 1 .000

1 . 338

1.497

1 .338

12-000

1 .238

1.226

1-238

1 3-000

1.147

1 .004

1-147

1 4.000

1 .062

0.823

1 .062

15.000

0.983

0.674

0.983

1 6.000

0.910

0.552

0.910

1 7.000

0 • 8 A3

0.452

0.843

18.000

0. 780

0.370

0. 780

19.000

0. 723

0.30 3

0.723

20.000

0.669

0.248

0.669

0.50000 NO. OF

INTERVALS

40*

PLOT OF Y C 2 >

Eiaaie fic — i tas

been set to zero) •

9>£ t&e respiratory tbXikl "lth U* ISflSS AftAi£lU&° e^imjQatgd £. [«] as

Rote the deeper inspiration and longer period.

Id general, one can translate directly from a aatheaatical flow diagraa like that of Figure
3 into the equations of section 8.0 of the second order Runge~Kutta routine of Figure 6a. Our
■ethod is to handle the Miscellaneous algebraic computations first, and then to write equations
for each of the integrator inputs in turn[6].

Since FOCAL is an interactive language and space in the mini computer is at a premium we
have not tried to write a completely general program (certain aspects of it, like the plotter in
section 6.0, Figure 6A, are changed to fit the needs of the particular simulation at hand). We
did try to arrange the program so that in each run all of the important parameters of the run
are displayed. Again, this is a decided advantage over £Ke analog computer* where a great deal of
cfoc umen t a ti on is left to the user.

On the other hand, as noted above, digital simulation in a higher level language is a slow
process; a run of 20 points as in Figure 6B or 6C would take approximately 2.5 minutes and cost
21 cents at our Divisional computing facility.

The example of Figure 6 is a qualitative one, designed to illustrate the redundant feedback
loops which must exist in the central nervous system to generate the respiratory rhythm. The
point of digital simulation in this case is to allow students to obtain a "feel" for the system
which they could not otherwise get.

A more complete use of the digital computer is made in the simulation of a system which is
quantitatively well described. Such an example is the respiratory model of Grodins, et al.
11954) cited by Rilhorn (1966).

The analog computer program given by Rilhorn shows eight operational amplifiers, two
integrators and a multiplier, tie have modified his diagraa into our notation, removing all of
the hardware aspects of the analog computer diagraa and also scaling constants. (Figure 7.)

This model has been programmed as a subsection of the Runge-Kutta routine and this section
together with a run is shown in Figure 8. The equations are direct translations of Milhorn’s
equations (5-10 through 5-12, page 74 of Milhorn, 1966). Our output may be compared directly
with that given in Figure 5-42 of Milhorn's treatment. It might be noted that in this simulation
we used a smaller step than previously, computing 10 points for every one plotted.

Table 1

Constants and Variables of the Two Compartment Respiratory Chemostat*
(After Grodins , ot al. (1954)}

Variable or
Constant

Initial Condition
or Value

Physiological Meaning

Y(l)

.052

Alveolar CO., concentration

Y(2)

.533

Tissue CC>2 concentration

KCD

.00425

Slope of C02 dissociation curve
(mmllg**1)

K(2)

.32

Intercept of C09 dissociation
curve

K(3)

3.0

Alveolar compartment volume
(liters)

K(4)

.01

Inspired C0? concentration

K(S)

760.0

Barometric pressure (mmHg)

K(6)

Lumped tissue compartment
volume (liters)

K(7)

.263

Metabolic C02 production
(liters/minute)

K(8)

471

Slope of VR vs Y f 2) curve
(liters/minute)

K(9)

246

Intercept of VR vs Y(2)
curve (liters/minute)

5.023

Alveolar ventilation rate
(liters /minute)

D(l)

Time derivative of alveolar CO.
concentration

D(2)

Time derivative of tissue C02
concentration

Non-dimensional normalized
response of VR

*The equation system for this model is given in the flow diagram of

Figure 7 or in the program equations 8.05-8.30 of Figure 8.

Two Compartment Respiratory Chemostat

(After Grodins et.al.)

ai»an* ln^w if horn5 /fqf * » tt*fiAjCii2£l SAglgSil* **>• aodal has b««n foraulatad j, >■ aquations
9i*»n in flxlhora (1946) attar a aodaL of Grodins at al. p9Su> loraal valuas o£ tha variablaa
and constants .ca qitra. in Xabla I. Tha aodal par.its xssa.tig.tio. ^o£ tha i.portanca^ ££
nuabar of paraaatars inflnancinq alsaolar vantilation rati. xsportaoca or 1 arqa

ERLC

2s . as

Figure £ iMMft-J
example shows the
veatilatioo rate
value within 5 or
computed Cor each

08.05 S VR=KC8)*YC2)-KC9)

08.10 S DC ! ) = ( VR* CKC4)-YC 1))*KU0)*(YC2>-CK<1)*KC5)*YC|)+KC2))))/KC3)
08*20 S DC 2)= CKC 7)+KC 10 )*CKC 1 ) *KC 5)*YC 1 ) +KC 2 l-YC2> > > /KC 6>

08.30 S Z = C VR-ZO)/CZI-ZO)

ENTER RUN PARAMETERS

ND> 2 IP#10 PN » 20 TS* 0 TO 20

SET CONSTANTS

ZO# 5-023 ZI 6.106
K 1 4.25E-3 0.004

K 2 .32 0.J20

K 33 3.000

K 40-. 01 0.010

K 5 760 760.00

:< 6 40 40.000

K 7 .263 0-263

K 8 471 471.00

* 9 246 246.00

K 10 6 6.000

INITIALIZE INTEGRATORS

1YCJ) .052
2YCJ) *533

TIME

YC 1 )

YC2)

VR PLOT OF Z

0.000

0.052

0.533

1 .000

0.054

0.534

5.379 *

2.000

0.054

0.534

5.640 *

3 . 00 0

0.054

0.535

5.806

4 . 000

✓j • 0 5 3

0.535

5.912

5.000

0.053

0.535

5.981

6.000

0.053

0.535

6.025

7.000

0.083

0.535

6*053

8*000

0. 0C 3

0.535

6.072

9 • 000

0.053

0.535

6*084

10.000

0.053

0.535

6.091

1 1 .000

0.053

0.535

6*096

12.000

0.053

0.535

6*100

1 3.000

0.053

0.535

6. 102

14.000

0.053

0.535

6. 103

1 5.000

0.053

0.535

6* 104

1 6.000

0.053

0.535

6* 104

1 7.000

0.053

0.535

6.105

18*000

0.053

0.535

6.105

19.000

0.053

0.535

6. 105

20.000

0.053

0.535

6. 105

0. 10000

NO. OF

INTERVALS

200*

utt. focu ijElaiaalatiai si ifei respirator? sAsifflttai isiai stl tiaasa 2- £*•

■o Itol* s response to a step Cros 0 to 1% CO 2 concentration of inspired air* The
rises in response to the step input, approaching close to its steady-state
6 aiautes. The prograe as given va a run oa a 4k word coaputer. Ten points were
point printed.

Such a aodel can be used in the laboratory to study a variety of aspects of the control
system. Answers to all of the following questions aay be obtained froa running the aodel with
the appropriate values of input constants:

1. How will the rate of alveolar ventilation be affected by:

increased

decreased

increased

aetabolic CO2 production?
cardiac output?
baroaetric pressure?
inspired CO2 concentration?

gain in the alveolar ventilation feedback loop?

Perhaps it is well to point out that these are indeed theoretics 1 questions, i.e. questions
concerning a aodel which aay or aay not accurately airror the behavior of the aniaal. (It would
of course be foolish Co be carried away by the siaulation into thinking that aanipulatlng such a
aodel was a substitute for aoiaal experiaentat ion. )

DISCUSSION

Difficulties in Prerequisites

One of the aajor probleas I have encountered in atteapting to introduce a quantitative
systeas approach into ay physiology course has been a feeling on the part ol many students that
they are not really qualified to cope with physical and aatheaatical concepts that the course
emphasizes. This is in spite of the fact that all the students are required to take courses in
physics and mathematics before registering for general aniaal physiology.

It is not uncoaaon for ae to find, however, that their physics course has oaitted a
treatment of one of the classical topics which we need for physiology. Two areas in particular
which seen to be getting short shrift in soae physics courses these days are hydrod ynaaics and
geometrical optics!

On the aatheaatical side I frequently encounter the following problem: namely, while
students are taught in a one year calculus course to differentiate and integrate analytic
functions, they do not even know hot to write differential equations, let alone solve them by
formal methods. I would, of course, I)e happy if ay students could siaply formulate the
equations, because I can show then how to obtain nuaerical solutions to then. But the problem is
generally at the initial step of writing equations.

In the face of these prerequisite difficulties, there is strong pressure to liait the
discission to qualitative material that is aore easily grasped, and, of course, soae compromise
aust Do made if the students are to benefit froa the presentation.

The problem is accentuated by the fact that there are soae students, engineers and
aat henat icians interested in physiological systeas, who do follow very well the quantitative
approach and are anxious to refine the models to a point well beyond what their classmates can
u nder stand[ 7 ].

Our past response to these difficulties has been to attempt to aake the mathematics easier
and to teach it along uith the physiology. We have clearly reached a saturation point however,
and aore recently we have attempted to shift soae of the burden onto other courses.

We now have a one credit course in interactive computer programming within the Division of
Biological Sciences which is in its second year. We will shortly be getting students into the
physiology lab who are not only trained in usinq the digital computer, but enthusiastic about
its use.

At the saae tiae the Division of Biological Sciences has been instrua3ntal in planning a
course in aathenatics for biologists which emphasizes equation systems and aatheaatical models.
Students of this course will presumably be more receptive to a systems approach in physiology
when they start cosing through.

What About Physics?

The problea with the classical physics prerequisites is a aore difficult one to handle.
(Perhaps this would not be true at another institution.) fly own belief is that we aust generate
soae good self-study aaterial in bite-sized packages to supplement our students* curriculum. On
the one hand it is impossible to take the tiae within a physiology course to teach the
fundamentals of, say, geoaetric optics, and even if one had the tiae, most of the students would

not hold still for it. But on the other hand, it is pointless to try to teach a student about ae
eye if he doesn't even know how a lens works, so th^re mat be soae way that a student can fill
these lacunae in his background rapidly at a tine when he is notivaited to do so. Hence ny
belief that individual self-study naterial affords a solution.

naturally, teachers at different institutions say find a different pattern of deficiencies
in prerequisites and different constraints on solutions which attenpt: to renedy then.

SOHfUBY

I have attenpted to show how we have used analog and digital conputation in teaching
quantitative systens analysis in general aninal physiology. That approach consists of (1) the
enploynent of a nathenatical systens notation sinilar to that connonly used in analog
conputation; (2) the physical realizations of such systens on analog conputing equipnent,
supplenented by the use of feedback anplifiers in physiological exercises as signal processing
equipnent; (3) the use of an interactive digital conputer in the solution of quantitative
honework problens in elenentary proqrans with no iteration or logical branching; (4) the use of
the digital conputer to obtain nunerxcal solutions to systens of differential equations.

I have discussed the difficulties of such a course which prinarily concern the disparity
between the prerequisite knowledge needed and possessed by its students, and I have described
soae steps which we have taken and are taking to alleviate these difficulties.

ACKNOWLEDGES BUT

Portions of the equipnent used in the work reported here were supported by Grant GY 6S0S to
Cornell University under the Instructional Scientific Equipnent Progran.

NOTES

1. Peter Steward (Stewart, 1970) has eloquently stated the value of quantitative nodels in the
physiology curriculua. 1 particular/ endorse his views on the salutory alternative they
offer to the "verbal reasoning which has characterized the classical approach."

2. A reasonable source for a "standard" analog conputer notation is that given in Blua (1968).

3* Our laboratory currently has one 15 anplifier analog conputer of type EAI 380 with

repetitive operation feature and X-Y plotter. Zn addition, we have a PDP-8L digital
conputer with teletype and A-D, D-A converter.

4. I have written a 30 page booklet on this aspect of prograaaing in FOCAL (Howland 1971) as

well as a FOCAL nanual (Howland 1972a). At the tine they were written, the FOCAL language

appeared to offer the nost conputing power on a snail conputer, and I believe that FOCAL is
still superior to nost aini conputer BASICS in power afforded the user.

5. Not all of our students* honework problens are done on the laboratory digital conputer. our
students have access to the Division of Biological Sciences* interactive conputing facility
which offers FOCAL and BASIC at alternate tines at four terainals on a reservations basis.
1 have described this facility elsewhere (Howland 1972).

6. We have found that Conte*s text on nunerxcal analysis (Conte, 1965) is very useful as a
source for algorithns in this area.

7. It should be candidly adnitted that sone of these students are nore knowledgeable in
applied nathenatics than their instructor. However, this is a connon situation in
physiology which, as one Gernan physiologist observed, "has been getting too difficult for
physiologists for the last 150 years." There are a large nunber of problens endenic to the
teaching of physiology which sten fron its position as the nost derivative of all sciences.
For exanple, teachers of physiology are faced with another enornous expansion of knowledge
on the biochenical aspects of their profession.

BIBLIOGRAPHY

(1968). Introduction to Analog Conputation. Harcourt, Brace & world, lac.

Blue, Joseph j.
New York.

Coaros# J. H. ( 1 945) • Physiology of inspiration. tsar book Sadical Publishers. Chicago.

Coats, S. o. (1965) • Blaaantary lassrical Analysis. BcGraw-Hill Book Coapaay. law York.

Gcodina# P. S. at al. (1954). tsspiratory iaaponsas to COo Inhalation# k Tbsorstical Study of a
lonliasar Biological Bagulator. J. kppl. Physiol. 2- *83.

Howland# H. C. (1972). k TQCkl Priaar# 2nd sd. klgabraic Laaguagss. Ithaca# Ban York.

Howland# H. Cm (1971). Solving Quantitatiws Hoaawork Ptoblaas with POCki. Division of Biological
Scisscss Is tsractivs Computing Facility. Corasll Onivsrsity. Ithaca# law York.

Howland# H. C. (1972b). (In prsss) • klgsbraic Language Instruction in ths Biological Scisncss
Curriculum at Corasll. dr. Collsgs Scisncs Touching.

flilhorn. H. r. Jr. (1966). Ths kpplicatioa of Control Thsory to Physiological Systeas. tf. B.
Saundsrs Co. Philadslphia.

Stsvart# Pstsr a. (1970). Coaputsrs in Undergraduate Physiology Tsaching. la Procssdings of
Coafsrsacs on Coaputsrs in ths Undsrgraduats Curricula# Con tar for Confsrsacss and
Institutsa# Ths Univarsity of Iowa# Iowa City.

COHP UTEBIZED ECOLOGY SIHULATIOI

Ernest (1. Salter
Cottey Junior College Cor vonoa
Nevada, aissouri

Gerald a. Pitts and Barry L. Batesan
University oC southwestern Louisiana
Lafayette, Louisiana 70501

Professors in the field of ecology have a difficult time in presenting to the undergraduate
student the ideas that make up the concept of genetic-environment interaction which are basic to
the study of ecology. At the University of Southwestern Louisiana , Lafayette, Louisiana, and
Cottey Junior College for Women, Nevada, Missouri, a simulation model has been developed which
allows a student to study such an interaction on a closed population of a single species or to
predict the results of such an interaction for various contemplated envionmental changes* The
model can b e activated by the professor or the student through one of the eight remote terminals
located strategically around the campus (University of Southwestern Louisiana only, Cottey
Junior College depends on distributed hard copy). By changing the input of individual factors
(individual gene content and dominant and recessive gene factors) and/or environmental
factors (population number, number of predators, food supply, water supply, age death chart, and
accident ratio) the student can receive direct feedback as to the genetic and environmental
results after a selected number of years*

The problem of determining the time (in generations) for a genetic variation to become
predominate is dependent on the weight factor which a certain genotype, or group of genotypes,
contributes to the survival of the individuals* Since different rates of producing variation
occur in nature, seemingly independent of the present, the model permits a variety of
environmental factors to interact with the genetic pool of the population on a weighted factor
basis* Thus the birth and death of individuals is based on the environment and the genetic make
up of the individual.

A genetic examination of the simulation should provide some insight into the working of the
model* The input consists of any number of individuals along with their gene patterns, tables
for the mating and birth routines and tables for each of the death routines* Death is provided
for by predators, lack of food, lack of water, age and accident*

In the sating and birth routines, each sale in the population is given a nusher of chances
to sate with a feaale, depending on the population size* For each successful sating, the litter
size is conputed fron the genetic characteristics of the parents and a litter size table. The
genetic sake up of the newly born individual is deterained by flendelian choice froa the parent
genes. After a successful sating, the feaale is tagged to prevent anting again within the saae
year.

After aating is coapleted, tho nuaber of predators for two years in the future is conputed.
The nuaber of predators is proportional to the nuaber of individuals that they feed on, but the
aodel uses a two year delay for the computed nuaber of predators to be engaged in the sodel*

In the predator routine, the individuals die according to the genetic doainant or recessive
character of genes which would have an effect on the predator avoidance of the individual* The
genetic structure, along with the nusber of predators, deteraines the nuaber of individuals
dying by this routine*

The next death routines, lack of food and lack of water will be discussed together because
of their siailarity. The current food and water supply are changed according to the present
population and a recovery factor based on the previous year's population. This is done in order
to reflect the fact of nature that the sore individuals there are the less food and water there
exists per individual and the slowness of recovery of the food and water supplies. For the
genetic characteristics which effect the ability of an individual to find or utilize food or
water supply, a death nuaber is calculated and used to detersine whether the individual
sur vi ves.

In the age routine, the death rate is deterained according to the age of the individual and
certain genetic qualities. The age table entered previously deteraines the death rate.

The accident routine provides for reaoval of individuals by a raodon, non-geaetic, non-
environaen tal basis by a percentage of the individuals in the systea at that aoaent.

xsLHI toe. ...

TABLE I

INTERNAL STATISTICS

PERIOD

YEAR

NUMBER

START

NUMBER

BORN

NUMBER

DIED

PREDATOR

FOOD

WATER

AGE

ACCIDENT

AGE

table

NUMBER food

1.52

1.53
1.52
1.52

WATER

SUPPLY

4.52

4.53
4.53
4.55

12 13 14 15

TABLE II

DOMINANT GENOTYPES PARTS PER TEN THOUSAND

MAU GENE2 GENE3 GENE4

4402 6044 7014

GENE9 GENE10 GENE11

7761 6417 8283

8432

GENE12

5373

GENE5

6865

GENE6

7611

GENE13

7611

GENE7

9029

GENE8

7835

GENE14

7089

GENE15

8582

RECESSIVE GENOTYPE, PARTS PER TEN THOUSAND

F£S -s -s "SB IS IS «8S “»

“ “S -gjj «s «JJ -Bj «•

TABLE II (CONTINUED)

DOMINANT

GENOTYPES

# PARTS

PER TEN THOUSAND

GENE2

GENE3

GENE4

GENE5 GENE6 GENE7

GENE8

GENE9

3619

4291

6268

3992 5597 6716

5074

4962

GENE10

GENE11

GENE12

GENE13 GENE14

GENE15

3768

5671

3395

5149 4776

6007

RECESSIVE

; GENOTYPE

, PARTS

PER TEN THOUSAND

GENE2

GENE3

GENE4

GENE5 GENE6 GENE7

GENE8

GENE9

6380

5708

3731

6007 4402 3283

4925

5037

GENE10

GENE11

GENE12

GENE13 GENE14

GENE15

6231

4328

6604

4850 5223

3992

The aodel has peraitted arbitrary selection of e&firoaaent and genetic weight factors. This
has allowed the users to ezaaine and re-evaluate the results with the aajor features of
interaction presently docuaeated. It also has peraitted the users to Bake predictions of
variations likely to be produced if the environeental and genetic factors of the species can be
reasonably deteraiaed.

Priaarily, the validation of the prograa was handled by the Biology Departaents of the
University of Southwestern Louisiana and Cottey Junior College for Noaea[1,2]. This aodel gives
the student a "feel" for the genetic development over a nuaber of years under varying
enviroaaestal conditions that could not be obtained through classrooa lecturing or laboratory
work. The student has the capability of answering his own guestioas by siaply posing the
guestions to the coaputer in the fora of specific input paraaeters aad receiving iaaediate
feedback as to the effects.

BEPBBENCES

1. Cordes, Private Coaaunication, University of southwestern Louisiana, Lafayette,
Louisiana, Hoveaber 17, 1971.

2. Goering, D. K., Private Coaaunication, Cottey Junior College for Hoaea,

Nevada, Bissouri, Hoveaber 29, 1971.

Problem: Diminishing Polygon Forms

COflPareR BAFRD imqoirt investigations IN biologt

Janes C. Horton, David S. Hinds and nary Ellen Burrows
California State College
Bakersfield, California 93309
Telephone: (805) 833-2123

All courses in Biology at California State College, Bakersfield, are taught in the inquiry
aethod. Students are required to take an elementary course in conputer programing, and this
ability is later used for creating aodels, and for analyzing and sumariziag data. He eaploy the
conputer in another fashion to overcoae the resistance of students to enploy arithaetic to prove
foraalas or to becone faailiar with the workings of a aatheaatical relationship. He have
devised several prograas which nay be used by students without any previous knowledge of
coaputer equipaent for the specific purpose of extending a foraula into areas not given in the
text. The student is able to apply a concept, quantified by the foraula, to various situations
of his choosing and thereby validate the expression in each specific case. When groups of
students use this technique for a nuaber of different exaaples, a later class discussion can be
used to correlate the extension of a foraula over a wide range of situations, verifying its
application without a large expenditure of individual effort. In this way, aa thenatical
expressions becoae a part of the student's vocabulary because he has used thea extensively
rather than accepted then by rote.

As an exaaple, the following foraula for rabbit-fox predation caae anonyaously to the
author. It has been used successively in several courses involving predator- prey relationships,
in the use of aatheaatical lodeling to predict outcoaes of population interactions, and as an
exaaple of population dynaaics.

Xj_ = x0 + (Ax0 - Bx0y0)t

VI = y0 + fCVoxo - “Vo)*

Verbally the foraula states that the nuaber of rabbits present at a given tine (xl) is equal to
the nuaber of rabbits found initially (xo) plus rabbit natality (Axq) less those rabbits preyed
upon by foxes (Bxoyo) • Sinilarly the foxes present at the sane tiae (y i ) are equal to the
initial nuaber of foxes (yo) plus fox increases resultinq froa reproducing parents existing on
rabbits (CyQXo) ainus those dying of starvation (Dyo). The foraula is siaple enough to be
readily understood by cost students and is still capable of considerable aanageaent. The
original values in the foraula of A, B, C, D are 4, 2, 3, 1 respectively, xo vas 6000, yo was
2530 and t was 0.01 with a printout every 12 cycles. The expression obviously is curvilinear so
an ipproxiaation of the curve was obtained by re-establishing new values of x-j and y ^ at unit
intervals of tiae (0.01) and printing each twelfth approxiaat ion. (For convenience in our
prograa every tenth value was printed.) It is possible of course to consider each unit tiae
interval as a generation, but we found it aore convenient to regard each tenth interval as a
generation tiae. (A copy of a publication given to the senior author included the above
inforaation as well as a progna for calculation, for printout and for a display of the output
as a graph. Unfortunately, the copy contained neither author nor publication source. Hence we
are unable to express proper credit, but it probably should be attributed to L. B. Slobodkin.)

Printouts of tenth intervals were plotted against population size by the student. Two data
cards were supplied, one for the constants A# B, C, D and one for initial population size. Once
tha prograa was operational, duplicate decks of cards were provided to groups of 2 or J
students. Local stored prograas would be better but in the absence of easy access to this
aethod, card decks were nuabared to prevent ais-operation due to shuffling. Individual student
groups were identified by separate job cards and they punched their own data cards. Persons
without experience at the keypunch aachines asked their colleagues to illustrate bow these night
be used, and all students had an opportunity to punch their own cards.

Our first use of this particular problea in an envir onaental population biology course
required that students apply tae foraula expression using different population sizes. Fixed data
cards for the constants were used and students were allowed to vary population sizes between one
and ten thousand. The figures they selected were individual and each group plotted their
printouts. Coaparisons were aide in a discussion session. After an early and initial variation,
tha students were surprised to find that curves for all populations were reaarkably parallel.
Froa this they reasoned (with help) that the relationship dictated by internal constants forced
a pattern of fluctuation which was not overcoae by population size. -This indeed, was the first
point we wished to sake. It is our opinion that the students were aore aware of this condition
by being forced to discover it for theaselves, than if we had told then this was so.

The second step was
which would be stable over
curves fro* their graphs
paralleled those generated
recognize that population
but regain in soie kind of

to xsK the students to predict those levels of fox-rabbit populations
tins. The students connonly selected an intersection of foz-rabbit
aid then placed these values in their progi^m. Again the curves
in the first output and the students were once lore forced to
interactions dictated that these situations would not beco*e static
a variable balance.

The third step was to allow students to change the internal constants at will. In this
case various proposals suggested the direction of the change e.g., suppose something increased
or decreased the rabbit birth rate (A), somehow success of fox predation varied (B) , the fox
natality or bir.th mortality changed (C) or fox nutrient requirements were altered (D) • In
groups, students were asked to generate reasons for changes in a constant and then to create a
series of curves by plotting tie resultant populations against the original (Table 1). Groups
increased or decreased a particular constant so that all variations aight be explored. These
comparisons provided insight of how minor changes could result in drastically altered population
patterns. Students speculated an situations which night bring about changes in constants and in
a fourth step, to predict the consequences of this change. A further condition was established
in which students were asked to predict the conditions required for stasis. The output allowed
verification of each student prediction and although none resulted in the static condition, the
students were aware of the Multiplicity of factors influencing any population level.

y Proa these kinds of inputs, further discussion led the students into exchanges concerning
dynamic balances, population interaction, the cyclical nature of population variability, and the
difficulty of estimating correct constants, without the stimulus of a progra* which they could
manipulate, the students would invariably have reiterated the formula and would have known
little of its operation. The problem selected was almost juvenile in its simplicity and yet the
individual flexibility to predict, to Manipulate the variables and constants, and to plot the
outcome produced in the stidents an unusually wide recognition of the forces implicit in
population interactions.

A similar project involved the Hardy- Weinberg formula in a genetics course. This formula
which is an expansion of a simple binomial predicts gene frequency in a randomly mating
population where gene changes do not take place, where the population remains constant, and
immigration or emigration does not occur. The Kar dy-Weinber g equation is:

(p + q)2 = 1

where p, q are frequencies of two alleles of one gene and where p ♦* q - 1. The formula is widely
used in all genetics courses and without exception, the students memorize the formula, and apply
it in situations without, perhaps, fully understanding its import. Using the same idea as
mentioned above, a program was concocted to provide the arithmetic machinery and printout with
the data cards being the only variable to be punched by students. At first students were asked
to verify that the formula does indeed predict gene frequency over long periods of time (50-100
generations) using individually selected gene frequencies and population sizes. Perhaps this
exercise was redundant in that students invariably received printouts with the same gene fre-
quency for the lengthy period and it is suggested that a shorter period of time might be more
profitable.

Once the students were convinced that these predictions were true, variations were
introduced. Gene freguency for each generation was changed to simulate the process of gene
mutation and the resulting changes in gene frequency were plotted. Selections for or against
certiin gene combinations were programmed and shifts of gene frequency were again plotted. The
influence of migrants entering the population with different gene frequencies was included and
lastly, gene drift was introduced using a random number generator and was used with different
gene frequencies. In each cise, the students selected constants which were in the usual range
encountered and were required to plot the effects of these gene changes over a period of 50-100
generations.

In a large sense, much of a genetics or population dynamics course can be built around the
programming. From those cases where population geae pools were constant, (egual to conditions
encountered on a small island* students were asked to illustrate the "founder principle" and to
relate its effects upon ensuing generations. Natural selection and evolution of traits were
included in this particular discussion and the students became aware that a gene pool consists
of a large number of individuals and breeding randomly. The next variation introduced was
mutation and students were able to plot changes in population size (in terms of gene frequency)
as a consequence of forward and back mutation rates. Because of the ability to see the effects
ot mutations over a large number of generations immediately, the students were aware of the slow
rate of gene freguency change under normal rate conditions ( 1 0“ 4 to 10”® /generation) . Students
would not normally be exposed to thisvisible evidence since they are reluctant at least, to

Table 1. An example of printout resulting from changes in the variables B and
C in the fox-rabbit predation formula. Only the maxima, minima and
amplitude from each situation are given. The figures represent the
change in each population from original value:.' of 6000 rabbits (x0)
and 2500 foxes (y0) . The two curves are not superimposed and the
time lag is that of the fox curve behind (in response to) the rabbit
curve.

Maximum Minimum Rabbit Maximum Minimum Fox Time

Rabbit Rabbit Amplitude Fox Fox Amplitude Lag

A B C D

4 2 13 6.186 1.168 5.019 3.759 0.892 2.867 0.320 (original)

" 3 " " 7.720 ' 0.773 6.947 3.042 0.421 2.621 0.290

4 " ” 9.827 0.445 9.382 2.819 0.200 2.619 0.260

" 5 " " 12.164 0.243 11.291 2.716 0.098 2.618 0.240

" 6 " " 14.634 0.129 14.505 2.658 0.049 2.610 0.220

4213 6.186 1.168 5.019 3.759 0.892 2.867 0.320 (original)

" " 2 " 6.046 0.124 5.992 6.756 0.248 6.508 0.240

" " 3 " 6.020 0.018 6.003 9.557 0.072 9.485 0.190

" " 4 " 6.010 0.003 6.008 12.171 0.021 12.150 0.160

M " 5 " 6.005 0.000 6.005 14.645 0.006 14.639 0.140

TABLE 1.

3*50

carry oat 100 separate arithmetic binomial expansions involving a slightly different gene
frequency change ia aach expansion. in tha next example where aalactioa against or for a
specific genotype occurred, students were able to see immediately tha affects of selection.
Populations, in terns of gtae frequency, decreased or increased aarkedly illustrating the
principles so often iterated to undergraduate students and so least often understood. , The
additional coaplicating factor of iaaigrants and emigrants in the population was also
illustrated graphically, partirulary when they were allowed to vary the auaber of nigrants per
population cycle.

Once these ideas were wall in hand, the value of the coaputer was; reinforced when students
were able to put together two or three of these separate changes to gene frequency ia the
population. Nutation under conditions of specific selection for the autant, nigrants with
seiected-for or selected-against characteristics, closed populations with selection against the
recessive, and the eaergeoca of doainant foras served to illustrate aore dramatically to
studentn the changes in population than lectures ever could have done. The full iaplications of
this type of prograaaing in tie teaching of genetics courses has not yet been explored, but the
possibilities seen endless. Costs per student in terns of conputer tine were approximately SO. 16
per prograa and each student (working in groups) ran 2-3 programs.

luaerous other axanplen ia quantitative biology are susceptible to iaaediate application of
this node of conputer inguiry. Be have initiated exaaples of lung-gill-oxygen exchange, muscle-
bone- leverage principles, diffusion over cell gradients, and the integration of taxonoaic
siaiiarities in prograas which allow students to explore the variabilities allowel in a
aatheaatical aodel of a syntem, and to relate these studies to physiologic, anatoaic, and
thought problems. Be feel confident that these prograas which provide students with an
opportunity to explore the parameters dictating a dynamic balance or organisnal capability will
play an iaportant part in enticing student involvenent and elucidating hither-to obscure
relationships. Be feel that an iaportant portion of the educative process is in the
incorporation of a working relationship of predictive foraula into the students personal body of
knowledge. In aost cases thesa relationships can be displayed most econonically through the use
of coaputer prograns. In the conparison of 100 generations of fruit flies versus 100 generations
of coaputer printout there is little doubt of econoay. Sinila^v that these relationships
should becone a working part of the student's vocabulary there is liVcle doubt. Be suggest thin
method as worthy of exper iaentation by other institutions and intend to eaploy it further in our
inguiry investigations.

COMPUTER ASSISTED ALGORITHM LEARNING IN ACCOUNTING

William F. Bentz
The University of Kansas
Lawrence, Kansas 66044
Telephone: (9 13) 864-4665

Introduction

The purpose of this paper is to present several hypotheses about the potential advantage ot
learning accounting methods with the aid of computers. A synthesis of relevant learning theory
principles forms the conceptual foundation for these hypotheses, and several examples serve to
illustrate computer assisted instruction* The focus is only on those accounting methods which
can be characterized by computer algorithms* Due to space limitations, many other equally
important aspects of accounting instruction cannot be considered here.

Background

While many innovative applications of computer technology have been developed tor
accounting instruction purposes, almost no attention has been given to learning theory concepts
implicit in these applications. The development of computer assisted instructional (CAI) [1]
materials for accounting is apt to be both haphazard and inefficient until a conceptual model of
the relevant learning processes has been developed. More precisely, we must have a conceptual
model of learning processes in mind in order to

(1) set specific instructional objectives that serve to guide the educational
pr ocess[ 2 ] ;

(2) formulate hypotheses, based on learning theories developed in other contexts,
about the expected contributions of alternative instructional aethods to the
set of instructional objectives;

(4) efficiently select CAI materials, based on their hypothesized benefits as
indicated by theories of learning, for turther development and experimental
testing; and even to

'5) investigate successful applications of CAI to identify the important elements
of these applications and to determine the nature of the success achieved.

In addition to having a weak conceptual foundation , many educators adopt such a limited
view of CAI that its development may be unnecessarily constrained. In accounting, the dominant
view of the computer is that it is a giant calculator. Thus, computers are viewed as a
particular type of instrument which serves one function - calculating [3]. A more inclusive view
is that computers are valuable teaching aids that can facilitate the learning process in many
ways, in addition to performing purely calculating f unct ion s[ 4 ]. The instrument view of
coaputers tends to limit their use to beginning courses, while a broader perspective is more
likely to result in the development of CAI materials at all levels of instruction.

The Structure of Accounting

The superstructure of accounting has been studied by several researchers, including Tjiri
[16], Mattessich [18] and Sterling [23]. These efforts involve attempts to describe accounting,
as practiced today, in as compact a manner as is possible. There are at least two practical
benefits of such efforts. First, by capturing the essential structure of accounting in a tew
axioms or laws, one can better communicate the essential characteristics of accounting to those
outside the discipline; and, secondly, one can more efficiently describe accounting to
prospective accountants.

However, at another level of abstraction, the structure of accounting can be viewed in a
less formal, and more limited way. The subject ot accounting is frequently explained by first
partitioning it into topical areas which are deemed to have a structure ot their own. For
example, depreciation accounting, accounting for leases, accounting for pension plans and many
other topics are discussed somewhat independently, in spite of the common superstructure which
describes all of financial accounting.

, 41

Bf shifting our focus from the superstructure of accounting to a lower level of
abstraction, accounting can be viewe! as a collection of algorithms which relate to particular
topic areas. "An algorithi is a procedure for solving a problem." [15, p. 1] In sore torwai
terms, an algorithi is something that can be carried out on an idealized machine, called a
Turing machine. Although the properties of Turinq machines have been more precisely defined,
let it suffice to note that a Turing machine can do anything a o tored-prog ran computer can do
[15, p. 170]. Therefore, for our purposes those procedures that can be performed by a stored-
program computer are called algorithms.

l!l£ jnce o£ Algorithms ifl &c£Ountjjig

flany accounting techniques can be characterized as algorithms; thus, the learning of
accounting techniques involves the learning of algorithms. Typically, the student reads through
a demonstration problem and notes the sequence of steps used therein. Then, the student works
several problems, mimicking the sequence of operations that are executed in the demonstration
problem. The sequence of operations (an algorithm) necessary to solve an examplar of a class ot
problems becomes apparent to the student during the process ot examining the demonstration
problem, or while working the homework problems. If the method is understood, it is understood
is a technique which is applicable to problems other than the particular one at hand. Thus, the
student who understands the method can apply it to a new problem with little difficulty, while
the student who rotely learns a sequence of operations to solve problem X may have difficulty
solving problem Y, even though X and Y arc of the same class of problems. Although other types
of learning may take place while one works problems, the learning ot accounting algorithms, and
the practice involved in applying them to specific situations, are the major functions served by
procedura 1- ty pe homework problems.

There are two additional reasons for focusing on accounting algorithms, in auditing, the
professional accountant is faced with the problem of evaluating the system of internal controls
tha; assures the quality of the accounting data on which an opinion must be rendered. Because
many accounting records and recording processes are being automated, modeling or flowcharting
the processing system is of utmost importance on almost every audit. Part of what is being
modeled or tlowcharted is the algorithm that represents the method by which a machine transforms
inputs into output. Therefore, the auditor must be prepared to deal with algorithms in their
general form, not with a particular solution method for test problem X. Precisely because the
clerical procedures performed inside the machine cannot be observed, the modeling ot these
unobservable algorithms is more important than ever before.

The construction aud testing of algorithms is an equally important function ot the
auditor's counterpart, the management consultant. In designing a new system, or in revising an
existing system, the management consultant must specify how activities are to be accomplished.
At some stage in the design process, a designer must specify the detailed procedures to be
executed by the system. This specification is, in essence, an algorithm even though the system
being designed may not be an automated system. Thus, for management consultants, the
spec: f icat ion of accounting algorithms is an integral part of the system iesign process.

L£d£ning flegoun t^ng Algofi t hms

Now that the importance of looking at the algorithmic nature of accounting methods has been
discussed, we can focus on three approaches to learning accounting methods: (1) The traditional
problem-solving approach, (2) reception learning of generalized algorithms, and (3) discovery
learning of generalized algorithms.

I &e tltiitiorial method. In treahman through junior level courses, the instruction sequence
usually includes the presentation of some concepts, propositions, and background information.
This material is followed by tne working of accounting problems which serve to clarity and
illustrate the concepts presented and the accounting methods involved. As mentioned in the
previous section problems involving a sequence of operations t^nd to be solved in one of two
general ways. First, if a demonstration problem is presented, the student tends to examine the
demonstration problem and then attempts to work a problem, or he attempts to work a homework
problem using a demonstration problem as a guide. In either case, the learner is actively
attempting to discover for himself the sequence of arithmetic operations involved in the
accounting method. Understanding of the method can be regarded as complete when the student can
apply the method to similar problems (application), or even to novel situations which have not
been related to the technique before (problem-solving learning as described by Ausubel[4]).

Several criticisms of the "problem" method of learning implicit algorithms are in order.
First, since the student never sees the algorithm in its general form, he may stumble through
several problems before understanding the methodology embodied in the indisclosed algorithm.
Second, the slower learner may not receive sufficient feedback from a tew homework assignments

to fully qr-isp the method. Third, the learning of a method by working problems may only result
in pre-verbal un:l°r stan d iny which cannot be retained as long as a verbally created description.
Fourth, even it a student learns a method by working proolems and can verbalize that
understanding, he may have difficulty remembering the more important features of the method
unless ho has the opportunity to work with an abstract model ot the method. Further, the more
general and clearly defint?d algorithms should be more easily remembered than a collection of
loss genoiai methods which are not clearly di f f erentia ble[ u , Chapter 5]. Fifth, there is a
tendency to teach business terminology and business practices by introducing them in assignment
problems. While learning about business practice is important, the super imposing of concept
learning, prospoui t ion learning and problem-solving may only confuse the student and impede the
learning of accounting algorithms.

learning of genera li zed algorithms. A second way of learninq accounting methods
i\ to encounter them in complete form, and then to apply the method, or algorithm, to particular
problems. The sequence of instruction would include a presentation of concepts, propositions and
hackqround information, as before, followed by a presentation of the accounting algorithm in
general form. After the algorithm is studied, it is applied to a series of problems which serve
to clarify the students* understanding of the algorithm, as well as demonstrating the range of
applications associated with the algorithm being studied. Each student’s understanding of the
algorithm is tested in the same manner as described above

Algorithms can be presented for reception learning by means of several different devices.
Flowcharts, decision tables and computer programs coded in procedure-oriented languages can he
used to describe almost any accounting procedure. As computer courses become required, these
tools become more and more familiar to all business students, so their classroom use is feasible
in many schools.

Note that these two methods of learning are very different. In the first case, the
algorithm must be inferred from an example, or from the feedback provided while the student is
attempting to solve problems "cor rect ly. " In the second method, the studen : learns the algorithm
by reception, rather than by discovery. The algorithm is presented in its final fora, so the
student noed not discover it foL himself.

There are severcil criticisms of the reception learninq method, as there were of the
traditional method. First, students may apply the algorithm to speciric problems in a rather
mechanical manner, which may not require them to think about the method itself. Second, even
when students think about the algorithm as a generalized technique, they may attain only a
pceverbal understanding of the algorithm. Preverbal understanding is only an intermediate phase
of the learning process and does not represent a terminal learninq objective. Third, the act
applying a specified algorithm to a set of problems may lack the motivational qualities ot a
problem or puzzle, that must be solved.

Presenting accounting methods as algorithms does have several advantages which alleviate
the limitations of the traditional method mentioned above. First, by focusing on the algorithm
itself, the instructor is telling the student what is important, in the process of solving
individual problems without knowing that a qeneral solution method exists, a student may not be
able to separate the important features of a homework problem from the trivial. Secondly, by
working with a defined algorithm, rather than attempting to discover the algorithm, a student
may be able to learn more about its structure and essential features because it has been fully
specified for him, in general form.

Another important reason for present algorithms is probably clear to most readers. Sono
ideas are simply vague and somewhat ill-delined until expressed in equation fora, or as
algorithms. For example, the time value of money is a concept which is readily accepted by
students on an intuitive level when first e/plained. After a careful and tedious presentation of
present value concepts, many students can handle straight-forward interest problems with the use
ot interest tables, but only the students with some mathematical sophistication seem to grasp
the process of discounting a series of payments to determine their present \alue. The ability to
work iwth symbols and equations seems to be necessary if a student is to understand interest
prob leras.

In summary, presenting accounting methods to students in the form of algorithms has certain
advantages over the more traditional problem solving approach. Specifically, it is hypothesized
that understanding is more nearly complete and retention is greater when students study and
apply explicity algorithms, rather than discovering accounting methods by solving problems.
This hypothesis is based on Ausubel's theory of the learning and retention of meaningful
mate r ia 1.

However, there are some disadvantages associated with reception learning. The ways in which
CAI can be expected to alleviate these disadvantages are discussed next.

Computer assisted discovery learning of acco^rntrnu algorithms. An alternative to reception
learning is the discovery learning of accounting algorithms. In contrast to solving a sequence
of problems, the assignment is to construct a general algorithm which then can be used to solve
a whole class of accounting problems. Text material, illustrative problems and handouts can be
used to specify the accounting method, but the student is forcc?d to generalize the method so
that an algorithm can be formulated. The algorithm can be characterized by flow charts, decision
tables, or an operational program coded in a language such as BA.SFT, FOPTHAN, or COBOL,

What are the potential benefits of having students reconstruct accounting algorithms by
writing computer programs? First, consider the potential motivational benefits. In the process
of writing a program, t.he student receives a lot of feedback which tends to support continued
work on the problem (a h y pot hes 15 ) • The feedback is in the form of error listings from the
computer and the computed answers to a test problem. Tf a student gets an incorrect answer, he
has a clear signal that his algorithm contains souie errors. Discussion with the other students
that congregate at the computer center and comments by the instructor also serve as valuable
feedback. Incidentally, it is relatively easy to follow the logic of a student's program when
the procedure being programmed is a familiar one and when a list of suggested variable names has
been provided as part ot the assignment.

Second, people tend to think about incomplete tasks more than they do about completed
tasks[4, o. 490 ]• Therefore, it is hypothesized that working on on"' computer program for N days
may maintain more concentrated student attention than working and completing several different
problems over the same time period. Another motivational aspect is the greater opportunity tor
satisfying ego- f u If ill i ng needs when the student must construct an algorithm which is not
presented to him in completed form. Constructing the algorithm is satisfying in itself, and
learning computer skills is satisfying to many students because ot the career opportunities
associated with a knowledge of computers.

One linal motivational benefit, is the opportunity to complete satisfactorily a task before
submitting it tor final approval. Some students find it very frustrating to spend hours working
complex accounting problems, Lo achieve only partial success. With programs, it enough lead time
is provided, diligent students have the opportunity to write satistactory programs.

The potential cognitive learning benefits of the process ot constructing accounting
algorithms are dependent on the claim that the student will thoroughly uniorstand an accounting
procedu* it he has written a computer program for it. Further, it is hypothesized that
understanding an algorithm is a higher level of abstraction than can be achieved by most
students in the process of solving particular problems. To th'J extent that these claims are
true, a s t u* nt's knowledge of the accounting procedure that he programm ?d should be integrated
into his cognitive structure as a generalized method which is clearly differentiable from other
accounting methods.

There are several conditions which can be expected to facilitate greater cognitive learning
behavior. First, t.lic construction of an algorithm requires more active participation in the
learning process than does the learning of an algorithm presented in the final form (reception
learning). Some students will critically evaluate new ideas to "make sense" out of them while
wonting at the task of incorporating them into cognitive structure. However, all too many
students are passive listeners when propositions or problem solving methods are presented to
them in final form. Therefore, to the extent that more active learning can be induced by
requiring students to construct algorithms, it is hypothesized that greater learning is to be
expected. Experience indicates that most students do need some inducement to become actively
involved in the learning process.

Second, the benefits of massed learning, as opposed to distributed learning, are related to
the learning of algor it h ms[ 5 ]. In this case, the alternative learning methods being compared are
the learning of accounting methods by solving individual problems as opposed to constructing
algorithms for subsequent application. In solving a sequence of problems, usually of increasing
difficulty and complexity, the student encounters two problems: forgetting between problem-
solving sessions, and the warm-up required to recall the methods and settle into the new
problem. It seems plausible that iiorgetting can be a factor since most undergraduate students
take rive or six different courses each semester, plus working and being involved in other
activities. Further, since accounting problems usually represent complex tasks, substantial
warm-up and reorienting ot one's thinking may be required each time a new accounting problem is
encountered. Under these conditions, massed learning can be more efficient than learning
distributed over a number of sessions.

Therefore, to the extent that there is a sizeable threshold of effort required to discover
and fully grasp accounting algorithms, the massed learnirq that is usually associated with the
writing of a computer program may be more efficient the. the solving ot a series of individual
problems over time. Because of the difficulties created by forgetting between problem-solving
sessions, and t.he warm-up required to settle into a new problem, it is being hypothesized that

the benefits of massed learning are applicable to the construction of computer programs, thus
improving learning.

Greater lateral transferability of knowledge Should also be facilitated by having students
write programs. Gagne[12, p. 235] theorizes that applying one's knowledge in a number or
different contexts increases transferability, although we know little about the precise factors
which are involved. A student can use his own program, or a previously written program, to solve
a variety of problems, thus emphasizing the generality of the techniques without increasing the
busywork that is usually associated with working a large nuoioer of problems. Thus, a student can
be encourayet] to generalize his conception of a technique.

12[iS 2l Computer Assisted Instruction

Process cost account ing, the allocation of service department costs among reciprocally
dependent service departments and operating departments, the allocation of profits among
reciprocally owned cor po ra t ions, corporate budgeting models, and the financial accounting
methods which involve present value calculations are all complex topics which involve
algorithms. For process costing, students can be given a set of program speci f ica t ions in order
to write programs which accept standardized inputs, and generate the required cost reports.
Students can also be asked to specify how the input data is to be collected, and how cost
reports are to be designed and distributed within a fictional company.

.Service department cost allocation techniques, profit distribution techniques, and
corporate budgeting models all involve using matrix operations to solve systems of simultaneous
linear equations. Their common structure becomes quite apparent to students when they program
these techniques. Similarly, the common structure of lease contracts, pension plans, bonds, and
long-term investments becomes apparent to students who have constructed an algorithm to rind the
present value of a single payment or of a series of payments. Moreover, students seem to
understand the present value techniques much better after having written such a program.

SUMMARY

In this paper, several learning theory concepts have been related to algorithm learning in
accounting. An examination of the relevant learning theory concepts leads to the hypothesis that
appropriate CAI techniques will facilitate the learning of accounting algorithms.

FOOTNOTES

1. No distinction is made between computer assisted instruction (CAI) and computer
extended instruction (CBI) here.

2. The importance of setting measurable objectives in education is well accepted
as is demonstrated by the comments of Church man[ 6 and 7], Goldi aaon d[ 1 3 ],
Ilommof 14 ], SvansflO], Gagne[12], and Ausubel[4].

3. The instrument view of computing is found in Anderson[3], Beams[5], Mastro[17],
Mecimore[ 1 9 ], Penick[20]. Person[2 1], CorcoranfH], and even

the committee reports of the AAA[ 1 ] and the AICPA[2].

4. See Cowie and Fremgr en[ 9 ] , Frank[11], Prater[22], and parts ot[ 1 ].

5. For a discussion of massed learning of low-level capabilities, see Stanley
Stevens[24, pp. 636-40 ], and Robert S. Woodworth and Harold Sch olsber g[ 26 , pn.
766-94 ].

REFERENCES

1. American Accounting Association Committee (1964) on Courses and Curricula —
Electronic Data Processing. "Electronic Data Processing in Accounting
Education," The Accounting Review, Vol. XL, No. 2 (April, 1965), pp. 4l2-2tt.

2. American Institute of Certified Public Accountants, Report of the Commit tee on

Education and Experience Requirements for CPAs. New Yorx: American Institute

of Certified Public Accountants, Inc., 1969.

3. Anderson, John J. "Integrated Instruction in Computers and Accounting,” The
Accounting Review, Vol. XLII, No. 3 (July, 1967), np. 563-66.

4. Ausubel, David p. and Ployd G. Robinson. School Learning: An In t roduc t ion to

fidugatiogaJL Psychology. New York: Holt, Rinehart and~Winston, Inc., 1969.

5. Beasa, Floyd A. 11 EDP and the Elementary Accounting Course, •• The Accounting

Review, Vol. XLIV, No. 4 (October, 1969), pp. 832- 36.

6. Churchman, C» West. The Systems A pproach . New York: Dell Publishing Conpany,

1968.

7. Churchman, C. West. "On the Design of Educational Systems." Working Paper No.

86. Center for Research in Management Science, University of California,

Berkeley, 1964. (Mimeographed)

8. Corcoran, A. Wayne. "Computers Versus Mathematics,*4 The Accounting Review, Vol.

XLIV, No. 2 (April, 1969), pp. 359-74.

9. Cowie, James B. and James ft. Freragren. "Computers Versus Mathematics: Round

2," The Accounting Review, Vol. XLV, No. 1 (January, 1970), pp. 27-37.

10. Evans, James.. "Behavioral Objectives Are No Damn Good," in Aerospace Education

Foundation, Technology and Innovation in Education. New York: Frederick A.

Praeger, Publishers, 1968.

11. Frank, Werner. "A Computer Application in Process Cost Accounting,” The

Accounting Review, Vol. XL, No. 4 (October, 1965), pp. 854-62.

12. Gagne, Robert fl* The Conditions o£ Lea£ning. New York: Holt, Rinehart and
Winston, Inc#, 1965.

13. Goldiamond, Israel. "Motivation-- Some Ways and deans," in Aerospace Education

Foundation, Technology and Innovation in Edu cation. New York: Frederick A.

Praeger, Publishers, 1968.

14. Homme, Lloyd. "A Behavioral Technology Exists-~Here and Now," in Aerospace

Education Foundation, Technology and Innovation in Education. New York:
Frederick A. Praeger, Publishers, 1968.

15. Hull, T. E. In troduct ion to Computing. Englewood clitfs, N. J.: Prentice-
Hall, Inc.., 1966.

16. Ijiri, Yuji. "Axioms and Structures of Conventional Accounting Measurement,”

The Accounting Rev iew. Vol. XL, No. 1 (January, 1966), pp. 36-53.

17. Mastro, Anthony J. "EDP in One Elementary Course," Tne Accounting Review, Vol.
XLII, No. 2 (April, 1967), pp. 371-74.

18. Mattessich, Richard. Accounting and Analytical Methods. Homewood, Illinois:
Richard D. Irwin, Inc., 1964.

19. ttecimore, Cbarles D. "Integrating EDP into the Elementary Accounting Course,"
The Accounting Review, Vol. XLIV, No. 4 (October, 1969) , pp. 837-39.

20. Penick, Jack G. ”ADP Equipment as an Accounting Teaching Tool,” The Accounting
E«view, Vol. XLI, No. 3 (July, 1966) pp. 549-51.

21. Person, Samuel. "The Integrated Use of Data Processing Equipment in Teaching
Accounting Subjects," The Accounting Review, Vol. XXXIX, No. 2 (April, 1964),
pp. 473-75.

22. Prater, George I. "Time-Sharing Computers in Accounting Education," The

Accounting Review. Vol. XLI, No. 4 (October, 1966), pp. 619-25.

23. Sterling, Robert R. "An Explication and Analysis of the Structure of

Accounting.” Working Papers No. 22 and 23 (Part Two) . Lawrence, Kansas: The

School of Business, The University of Kansas, 1969.

24. Stevens, Stanley S. Handbook of Mental B-^XCnol oqy. New York: John Wiley

6 Sons, Inc., 1951.

25. Williamson, J. Peter. "The Time-Shar ir.g Computer in the Business School

Curriculum,” Paper presented at the Kiewit Conference, Dartmouth College,
Hanover, New Hampshire, June, 1971.

26. Woodworth, Robert S. and Harold Scholsberg. Experimental Psychology. Now

York: Holt, Rinehart and Winston, 1965.

U£

THE BUSINESS CORE INTEGNATOi
AT INDIANA UNIVERSITY

Thoaas L. Guthrie
Indiana Univeraity
Fort Nayne, Indiana 46805
Tale phone: (219) 483-8121

In the acadeaic year 1966-69, faculty at the School of Buaineas, Indiana Univeraity,
Blooaington Caapus, began exper iaentation with a thoroughly reviaed undergraduate curriculua
which included what has been called the four course integrative core. The core is taken by firat
seaester Junior class standing business students who aeet specific prerequisites. The core
consists of three principles courses in the functional areas of finance, aarketing and
production and a new course, Siaulation of Business Enterprise. The conception and developaeat
of the core . by the faculty, spearheaded by Dr. williaa B. Panacher, reached such a stage of
aaturity by the acadeaic year 1970*71 that the Aaerican Association of Collegiate Schools of
Business awarded Indiana University School of Business the prestigious western Electric Fnndvs
award for educational innovation in higher education for its outstanding undergraduate core
prograa. The purpose of this paper is to describe the objectives of the integrative core,
deaonstrate the procedures involved, and relate the experiences and reactions to date, with
priaary eaphasis being given to the unigue part that the Siaulation courae plays ia the core.

Objective

Given the overall objective of the Business school to graduate students capable of
contributing to society in general and the business coaaanity in particular, the iaaediate
objectives of the four-course integrative core are:

1. to provide the junior year business student with a rigorous
and integrative education in the functional areas of business.

2. to provide a simulated business experience that will cause
students to begin to think like businessaen, to identify
theaselves with business and to increase their enthusiasa
for a business career.

3. to provide for the student a snail group ataosphere facilitating
the change froa a passive educational experience to one of
involveaent and action.

4. to provide the student the further advantage of snail size classes and a
closer student faculty relationship in at least one of the four core
courses (4) .

Prerequisites to the core, in addition to Junior class standing, include the following:

Principles of Econoaics.

Econonic Statistics. •• 3

Pinite Hatheaatics . . . 3

Calculus ..3

Introductory Psychology. 3

Principles of Sociology. 3

Hinageaent Accounting. ••••• 6

Legal Environaent of Business 3

These prerequisites, which are strictly enforced, provide the student with a higher level of
coape tency and consistency than had been required heretofore, tbus allowing a aore rigorous
treataent of subject aatter in the basic functional areas of business.

lagleaentation overview

The siaulation course is paraaount in aeeting the objective to integrate the students'
initial work in business decision-aaking. A coaputerized business siaulation gaae is utilized in
the course which is, of course, nothing new, since auaerous business courses use coaputerized
qaaes of one type or another. What is unigue is the relative iaportance of the gaae in the

course. Iq lost busiaess courses gases are used as sidelights to demonstrate principles or to
reinforce desired learning patterns. In the Indiana Simulation course the game is literally the
course, and sidelight assignments are made in conjunction with the other three courses.

To administer the game, the students are divided into teams of 4 to 8 people, each, which
comprise individual companies for gaming purposes* This is, again, not unique, bat what is
unique is that (1) individual team members attend the same section of all four core courses and
(2) all four core courses must be taken concurrently.

By utilizing the team approach and the business simulation game as a central classroom
activity, demanding the knowledge, analytical tools and methods taught in the other three
courses, integration is achieved in several ways:

First, as a result of each team being in the sane section of finance, marketing
and production, each student is a member for the entire semester of a small
management group which is responsible as a group for several assignments* The
management group is bound together by common goals, especially with respect to the
Simulation course. This, in effect, provides every student with 3 to 7 counselors,
tutors and friends, business and social. The advantages of this type of atmosphere
should be self-evident in these days when many universities and programs are being
charged with interest only in bigness and its often alleged counterpart, anonymity.

Second, principles being taught in marketing, production and finance are
reinforced through specific related assignments made in conjunction with the
Simulation course. Such assignments seem far more relevant and urgent to the
student than the typical potpourri of problems at the end of the chapter in
textbooks.

Third, the integration and assimilation by each student of knowledge in
marketing, production, and finance into a management philosophy is fostered. Since
each team is required in the Simulation course to make several marketing, production
and financial decisions over an extended period of simulated time, it must do so from

delicate quality c

Fourth, integration is achieved not only with respect to the student, but the
faculty, also. For the integrative core to be successful, there must be serious
planning and coordination of individual course topics, assignments and examinations.
As a result, duplication of subject matter is eliminated and more importantly, gaps
are closed. Overloads are coordinated. By precept and example, faculty show their
acknowledgement of and respect for all functional areas, regardless of their
specialities, and particular research interests.

Implementation Details

The implementation details of the integrative core will be discussed primarily from the
point of view of the Simulation course. As a matter of review, a business simulation or game may
be defined as a sequential decision-making exercise structured around a model of business
operation, in which participants assume the role of managing the simulated operations[ 2 ]•
Business simulations abound today, but few are both sufficiently complex and comprehensive to
provide the basis for a one semester, three credit hour course. One that does meet both criteria
is INTOP (International Operations Simulation of the University of Chicago) developed by
thorelli and Graves[ 6, 7 , 8 ]. Of course, the purpose of this paper is not to report about INTOP;
however, the reader must have some conception of the character of INTOP, if he is to appreciate
the role that the Simulation course is capable of performing in the integrative core. The
"typical" business simulation can he represented in a 1000-2000 card FOBTRAN program. The INTOP
model is represented in approximately 9000 FORTRAN cards* If one makes the dangerous assumption
that there is a direct relationship between the number of cards and game complexity and
comprehensiveness (and realism) , INTOP and the few models like it are in a separate league*
INT0P is not a program to be "dumped-on" the small departmental computer one day and processed
the next day. INTOP is international in scope and allows fundamental decision-making in all
functional areas of business except production balancisq and raw materials purchasing.
Environmental parameters may be changed so as to emulate segments of recent international
economic activity* Typical computer output in the form of financial statements, marketing
reports and ancillary data is shown in Illustration 1.

Procedurally, the Simulation course meets i;i 75 minute sessions twice a week for 15 weeks.
Individual sections are limited to nine teams. The first few class sessions are used to explain
the purposes and mechanics of the course and then the course is divided into two separate, but
related parts, occupying the two weekly class sessions. (

One session can be described as open company meetings; that is, teams (companies) are in
open session analyzing operations and results, formulating plans and otherwise getting ready tor
their new round of nanagemant decisions which are made on a weekly basis (and represent one

an interrelated

effectively. The learning of that

ILLUSTRATION 1. SAMPLE INTOP C*JTPUT.
COMPANY 1

INCOME STATEMENT

STANDaRO SALES
CONSUMER
INTRA-COMPANY
INDUSTRIAL
LESS-COST OF GOOOS
GROSS MARGIN
DELUXE SALES
CONSUMER
INTRA-COMPANY
I NOUS TRIAL
LESS-COST OF GOOOS
GROSS MARGIN
TOTAL GROSS MARGIN
operating EXPENSES
CONNER. ANO AOMIN.
ADVERTISING
SHIPPING
INVENTORY
SALES EXPEDITING
METHODS IMPROVEMENT
DEPRECIATION ANO FIXED
NET OPERATING FXPENSE
NET EARNINGS FROM OPER.
TOTAL NET OPER . EARNINGS

NON-OPERATING INCOME

INTEREST INTERCO. LOANS
L I CENSE S-X
LIC6NSFS-Y
MISC. INTERFST
TOTAL NON-OPER. INCOME
NON-OPFRATING FxPENSE
MARKET RESFARCH
LICENSFS-X
LICENSES-Y

R ANO 0 NFW PROOllC T X
R ANO 0 NFw PRliDllCT Y
TOTAL INTERFST
TOTAL NON-OPER. EXPENSE
GROSS EARNINGS
LESS-TAXES

LESS-CAPITAL TRANS. TAX
NET EARNINGS
LESS-OI VIOENOS
TO RETAlNEO EARNINGS

BALANCE SHEET AREA 1

ASSETS
CASH

A/R FIRST QUARTER
A/R SECOND QUARTER
INVENTORY STANOARO X 260630

OELUXE X 0

STANOARO Y I910IB

OELUXE V 66fc9B2

TOTAL

SECUR I T! ES

TOTAL CURRENT ASSETS

NET PLANT ANO EQUIP*

INVESTMENT INTERCOMP.

SUBSIDIARY CONTROL

TOTAL ASSETS

LIABILITIES

A/P PfRST QUARTER
A/P SECOND MARTEN
SUPPLIER CREOIT
AREA BANK LOANS
TOTAL CURRENT LIABILITY

LOANS PAYABLE

TOTAL LIABILITIES

STOCKHOLDER EQUITY

CONNON STOCK AT PAR
PAiO IN CAPITAL
RETAlNEO EARNINGS
HONE OFFICE CONTROL

TOTAL EOUITV

TOTAL LIAB. ANO EQUITY

INTflP - UNIVFRSITY UF CHICAGO

area

AREA

3 HOMfc

DUCT *

PRODUCT Y

PRODUCT X

PRODUCT Y

PkiJOnCT x

PRODUCT Y

726000

1 131661

49132ft

1 2 AftAft 0

313791

22754.6

3? A71 ft

1 3 A 309

297072

1361 7

500454

6060 A3

357018

96lA0fl

300276

500454

ftOftflA 3

36701ft

96140ft

300276

110061

112006

7A29H

109/36

56ftfc2

53000

70000

AO000

61000

23000

4BD00

3A057

I A9R

3437

10000

15000

5000

ftOOO

215000

190000

100000

146000

A 36861

A29063

220795

317173

79862

63592

377700
AA 1 3 72

136223

63423b

77046ft

22041 3

-0

220413

PERIOD 6

3913160

997162

2915997

29 1 599 7

4.6 W62
249000
AftOOO
3ft992

3H000
660000
1 663754
U3224.3
14322 4 3

1000

127M)

14760

1000

100 0

12760

14760

72000

99000

94000

\ 71000

1 mood

44 2.372

7714.6ft

22041 3

-|6«?5»>

12/ *>94 ^

230034

347166

6M?<.

•1

64- Vll 1

212339

42430?

1 6428*1

- \ 6H'6()

6 12680

212M9

42430?

1 64289

- ) SM/6h

632680

AREA 2

AREA 3

home office

CONSOLIDATED

12757

260351

106257

110793

490156

1115737

476189

143379

1735305

521942

125517

647459

116060

17018

353492

1117431

406570

1604002

100000

750000

950000

2345925

1045053

375152

060793

5426923

5160000

5000000

10160000

1 1095000

7505925

6045053

375152

12755793

16586923

TB54B1

477078

66124

1320603

1378 49

137869

705401

614947

66124

1466472

3300000

785401

614947

66124

3300000

4766472

10000000

395524

705106

184028

-544207

020451

6325000

5445000

125000

6720524

6230 1Q6

309020

9456793

10020461

7506925

6045053

375152

12756793

165H6923

ERIC

ILLUSTRATION t, CONTlNUCO.
COMPANY 1

INTOP - UNIVERSITY OF CHICAGO

PERIOD 6

ANCILLARY OATA

STANOARO SALFS UNITS
CONSUMER

intra-company

industrial

AREA 1

PRODUCT X PRODUCT V

AREA 2

PRODUCT X PROOUCT V

28000

8000

OELUXE * SALES UNITS

CONSUMER 0

INTRA-COMPANY 0

I NOUS TRIAL 0

NFG, COST ANALYSIS

PLIU STANOARO COST 117351

UNITS 18000

OELUXE COST 0

UNITS 0

PL ( ? I STANOARO COST 1*3280

UNITS 20000

OELUXE COST 0

UNITS 0

PL I 3) STANOARO COST 0

UNITS 0

OELUXE COST 0

UNITS 0

STANOARO GRAOE 0

OEUIXE GRA06 0

INTRA-CD* purchases

STANOARO COST 0

UNITS 0

DELUXE COST 0

UNITS 0

INOUS TRIAL PURCHASES

STANOARO COST 0

UNITS 0

OELUXE COST 0

UNITS 0

ENOlNG INVENTORY

STANOARO UNI TS 38000

GRAOF 0

OELUXE UNITS 0

GRAOF 0

NO* REG* SALES OFFICES l

max* Grade of imprivhmfni o

10859

66*982

32000

1 11*1
0

32000

158*9

106071
1 3000
0
0
0
0
0
0
0
0
0
0
0
0

179

20808

353*92

21000

1 192
0

21000

AREA

PROOUCT X

8965

8000

PROOUC T Y

market RESEARCH 1 area 1

PROOUCT x

PRICES POSTEO THIS ORT. STO. OH.

COMPANY NUMRER 1 26 -o

COMPANY NUMBER 2 12 -O

COMPANY NUMBER ) ft -O

COMPANY NUMBER * -6 -o

COMPANY NUMBER 5 f* -O

COMPANY NUMBER 6 60 -0

COMPANY NUMBER 7 30 -O

COMPANY NUMBER • 20 «0

COMPANY NUMBER 9 2J-0

GRAOES MEG. EOR NEXT ORT.

COMPANY NUMBER 1 0 -O

COMPANY NUMBER 2 01

COMPANY NUMBER 3 0-0

COMPANY NUMBER * -0 -0

COMPANY NUMBER 5 *01

company number t o -o

COMPANY NUMBER 7 01

COMPANY NUMBER 6 -0-0

COMPANY NUMBER 9 01

AREA 2

AREA 1

PROOUCT

TO.

DEI.

STD.

DEL.

STD.

DEL.

STD.

DEL.

STD.

DEL.

-0

-o

-0

-D

-0

-o

•5

-0

-o

-0

•5

-0

-o

-0

-o

-0

-i>

-0

NOTE. -0 OENOTES NO PRODUCTION. 0 OENOTES THAT ZERO* IS THE GRAOE BEING MANUFACTURED

-0

-o

-0

ERIC

G±

(LUSTRATION t. CONTINUED.

COMPANY

INTOP

- UNIVERSITY OF

CHICAGO

PEKluO 6

MAR RE 1

research

. AREA

AREA

PROOUCT

PRD0OC1

PROOUCT

PRODUCT

SALES THIS OUAATCAIOOO)

STD.

on.

STD. 1

DEL.

STO.

DEL.

SID.

DEL.

SID.

DEL.

STO.

DEL.

COMPANY

NUMBER

20.0

0.0

10.9

0.0

15.8

0.0

20. B

D.O

9.0

D.O

0.0

COMPANY

NUMBER

10.6

0.0

22.2

0.0

1 7.0

0.0

28. 0

0.0

company

NUMBER

17.1

0.0

16.7

0.0

20.0

0.0

7.1

0.0

company

NUMBER

0.0

7.0

37.5

0.0

19.9

0.0

D.O

0.0

company

NUMBER

34.9

0.0

35.7

24.4

0.0

company

number

0.0

6.7

6.0

0.0

4.6

6.5

0.0

Company

number

IS. 9

0.0

12.3

0.0

7.6

0.0

22.9

5.4

0.0

COMPANY

number

1.3

0.0

5.4

0.0

18.2

0.0

R.2

0.0

COMPANY

number

35.9

D.O

28. 5

0.0

U.9

0.0

26.0

0.0

TOTAL SALES ( 000 )

144.6

0.0

137.3

67.8

90.2

0.0

150.3

11.9

16.1

0.0

quarter of business operations) • The role of the instructor is to visit each team and, aided by
managerial accounting data and statistics (to be explained later) froii all previous quarters of
company operations, to prod and question each regarding analyses, strategies, tactics and
specific decisions for reacting previously established company objectives. The instructor, of
coarse, aids companies having specific questions and/or any difficulties with analyses they
should be able to do at any given tine during the semester. The open class session also provides
a convenient tiae for companies to negotiate all types of inter-coapan y deals including
industrial product sales, product licensing, leasing of facilities and services, etc. INTOP has
sufficient flexibility to accoaaodate practically any intercompany transaction imaginable.

The other weekly session is aore traditional, being devoted to instruction. The subject
Batter includes planning, controlling and the decision-making process. Considerable tiae is
devoted to bringing the functional areas of aanageaent into focus, and integrating then with the
operational decision- making taught in aarketing, production and finance. A skeletal course
outline is shown in Illustraiton 2. The topical presentation order in Welsch[9] is extremely
complementary to the developaent of the lecture schedule and the sioulation.

The first two to three weeks of the course are involved with explanation of the INTOP
environment, learning of the specific rales and development of philosophy, objectives and
organizational structure by each conpany. The fourth week the first round of decisions is due
and then one round of decisions is due each week thereafter until a total of 12 quarters (J
years) of operations have been simulated. (Actually only 10 sets of decisions are completed;;
the first set of decisions is for three quarters of operations. It takes two quarters to build
production facilities and one quarter to aanufacture products, so product aarket interaction is
not begun until the fourth quarter.)

Coanenciog with the first lecture on planning and control, a second conputer program is
processed with INTOP. The introduction of this sunaary analysis[5] is unique to ganing and has
so enhanced the course that it warrants specific discussion. The program is run in conjunction
with the INTOP program and subsequent to it; saaple output is shown in Illustration 3. The
instructor gets a copy of the suamary analysis for all teams and each teaa receives a copy
pertaining to its operations, linus the sumaary rankings; these are on the instructor's copy
only. The program solves two problems. First, in order for companies to make the aost
intelligible, rational, objective INTOP decisions, it is necessary for them to generate a aass
of aanagerial accounting data, in addition to the ancillary data that is a part of the regular
IMTOP output. The generation of these data required students to engage in busy work that (1) did
not enhance their learning and (2), in fact, limited even further the amount of tine available
for true decision-making. In addition, the logical argument was forwarded that in the "real"
world, managerial data would be systeaatically provided on a timely basis by the accounting
department of the company. Note the wealth of detailed sales, production, inventory, financial
and cost accounting inforaation arranged by geographical area in the sumaary analysis. This type
of information measurably enhances managerial decison- making. The second problea was concerned
with the systematic and periodic analysis of each teal's progress and problems. The aaount of
INTOP output generated weekly by a nine team section of Simulation of Business is voluminous. In
order for the instructor to provide a meaningful critique for each team during the open session,
the analysis of the output by hand was jast too burdensome. The output format of the summary
analysis is so arranged that the instructor can easily trace performance of a teaa in any
particular aspect of the simulation by just reading across the appropriate page and line(s).
Teams are required to submit forecasts by geographical area of sales, cash, production costs and
BOI (return on investaent). The weekly forecasts, first described as a written assignment for
week five in Illustration 2, are required for every quarter of simulated operations. Any
resulting high forecast errors tend to flag, automatically, problems that a team is having with
particular aspects of the simulation. Armed with summary statistics, forecast errors, relative
rankings and a complete historical summary of each company's operations, the instructor
efficiently prepares for his conference with each team during the open session. Problea areas
are quickly uncovered so that therapy aay begin.

A secondary benefit resulting from requiring each team to make quarterly forecasts should
be aentioned. The benefit is tiat guessing is practically eliminated. If a particular forecast
of a team is in serious error, the first thing the instructor asks the team during the open
session is to review with him the particular analysis that produced the forecast. Having none

ILLUSTRATIO:; 2.

Business Simulation Course I.VTOP Related Lecture Schedule

!-'cck

1-2

14-15

Topics

Business Philosophy
and Objectives

Organizational Structure

development of Specific
Coals and Strategies

Sales Planning and Control;
Forecasting

Production and Inventory
Planning

Planning Expenses-*?!anuf acturing
Overhead, Distribution and
Administrative Expenses

Planning and Controlling Cash,
Dividend Policy

Planning and Controlling
Capital Expenditures

Development of the Annual
Profit Plan

Cos t -Volume-Prof it
Analysis

Variance Analysis

Demand Analysis and Price
Setting

Company Audits

Assignment

Company Philosophy
and Objectives

Company Organizational
Chart and Individual
Job Descriptions

Company Goals and
Strategies

Forecast of Sales,
Variable Costs, Net
Darnings , Cash and
KOI for each Quarter
of Operations

Formal Proposal for a
Major Capital Expenditure

Annual Profit Plan for
Next Year of Operations

Cos t-Volune-Prof it
Analysis Supporting
an INTOP Decision

Variance Analysis
of One Marketing Area

Demand Analysis for One
Product in One Market Area

Oral Presentation
of Audits

proves to be very embarrassing* Also, in order to do an acceptable job of forecasting, teaas
■ust engage in a systematic analysis of the variables that impact on the particular variable to
be forecast*

The topics covered in wmeks six through twelve are traditional and should need no farther
explanation here* Of course, the point to reiterate is that each, of these topics is
suppieaentary to the simulation and is presented as just another aid to improve the decision-
making that each company is required to do*

The topic of demand analysis in week thirteen does warrant specific discussion* 1 think
many business students, as a result of their classroom training, are convinced that the concept
of a demand curve is one of those theoretical constructs which does not really have any
practical value in aiding business decision-making* By week thirteen teams have generated
sufficient data to plot a demand curve which is very aesthetically appealing in terms of fit* It
is a real joy to watch students rediscover (or discover) one of the basic principles of
economics and to determine that the principle is applicable to the simulated world in which they
have been operating (which by this time in the semester is as real to the students as if they
were running 6(1 or IBS).

The last topic, company audits, also deserves comment* At the completion of three years of
simulated operations, each company's records are turned over to an auditor (which is, in
reality, one of the other companies) • Records include, in addition to the standard financial
reports produced as part of the INTOP output, reguired charts, graphs and brief narratives of
salient discussion points covered prior to each decision* The auditing company is asked to do a
complete audit in terms of management, finance, production, etc*, culminating in a 15-20 minute
oral presentation* Given the benefit of hindsight and a semester's practice at decision-making,
an auditing team quickly flags the "boners'* and the quality decision-making of the audited
company* To insure that students never forget for a moment the need to plan for the future,
each auditing team is asked to make a minimum of three specific major recommendations to the
future management of the audited company*

£££&as

The team being the basic decison unit (rather than the individual) is reinforced in the
grading schema for the Simulation course; overall team performance accounts for 40 percent of
the course grade* The paramount danger here, as with most simulations, is to reward intuitive
behavior too generously* The rewards should go to the teams mastering sound management
principles, prescribed analyses, etc* But, on the other hand, those teams that practice these
principles and analyses and combine them with intuition, yielding a superior strategy, should
also be rewarded* I will not argue further as to whether it is "how you play the game** or
"whether you win or lose" that is important in terms of learning* Personally, 1 mix the two in
equal proportion* One-half of the 40 percent is based upon INTOP written assignments -
development of team philosophy, objectives, strategies, goals, analyses, sound forecasting
methods, etc* Each visitation during the open session has been institutionalized via a simple
summary performance sheet on which the instructor evaluates the quality of decision-making

during the last quarter of operations* The other one-half of the team grade is based upon team

performance vis-a-vis other teams* This is a particularly difficult grade to quantify because
(1) it is fraught with all the perils that real companies have in quantitatively measuring
performance and (2) the instructor needs to maintain consistency from one semester to the next*
For example, does one utilize return on sales, return on investment or return on total assets as
the quantitative measure of performance[ 1 )? Also, how does one guard agaiast the possibility of
the "last place" team this semester being "better" than the "first place" team the semester
before? If the same aggregate profit potential were generated each semester by the simulated
environment, then objective measures of level of performance could be ascertained after a couple
semesters* In INTOP, the economic environment is changed every semester to (1) prevent previous
class notes on INTOP being of any value and (2) to emulate a recent period of economic activity
to gain even more realism* Each environment has a different aggregate profit potential that is

really not measurable, a priori. In an attempt to negate some of these problems, I use the

following grading procedure for~this portion of team performance:

1. Rank teams according to the sum of their retained earnings and paid in capital
as of period 12* This is a measure of each team's leadership position in the
industry, based upon results to date*

2* Bank teams according to their average return on capital over quarters 4-12*
This is a measure of each team's efficiency in utilization of capital,
regardless of source or how much they use*

3* Bank teams in their average plant and equipment investment over quarters 8-11*
This is a measure of each team's potential ability to do competitive battle in
the future*

4* Take the 80th percentile team (iu terms of number of teams particpating) and
assign the team with that ranking a 100 percent rating* Calculate the

H LUST RAT If IN 3. SAMPlF INTDP ANALYSIS REPORT - I MO I A NA UNIVERSITY STHOPI HE
BUSINESS - COMPANY 2. r

PTR 1 UTR ? OTR 3

********* AR£A 1 (US)

EC ON

index x

SALES X STP-ORD

consumer

pricf

OTHER
PRICF
T I ! T A L
FORECAST
PC T ERROR
SALES X t'LX-GRD
CONSUMER
PRICE
FORECAST
PC T ERROR

For FAC.M A UP 1 T 1 ( iNA L OUARTt0
OF S I M ( i L A T E 0 (IP E P A T I PN S
ANOTHER COLUMN (IF PAT A
IS APOFP TO THE RIGHT HAI\lu

si of of this repupt. note

THE FASF WITH WHICH THE
PWllGRFSS HE THE COMPANY MAY
RF FOLLOWED.

prupuct y = pad j us

PRUPl'CT Y = VACUUM CLFANERS

OTR 4

OTR 5

] .06

1 .07

1 ft?n 3

1 ft 98 5

2 5

1 h?o 3

1 ft9ft5

1 6000

] soon

13.77

1 3 . 2 3

OTR 6

I .0?

1 057?
•*?
6000
I ft 5 7 2
1 ft 5 7?
I o ooo
-1? .7P
I

642ft

l*non

- 5 9 . P 4

EC On I NO EX Y

sales Y STP-GRI)
CONSUMER
PRICF
FURECAST
PC T EPROR

AOVFPT I S INC

PRoour.i x

PRODUCT Y

SALES OFFICES
C AND A COSTS

X actual

X OPTIMAL

Y ACTUAL

Y OPTIMAL

AVG COG SOLO
X STO OR 0

X olx-grd

Y STO-GRO

MFTHOUS I \* PRI IVFM FNT
PRODUCT X
PRODUCT '

.03

.97

• q 1

3i noo*

30 50 P

2 P90P

4 4

2 9000

2 900 0

20500

6.90

5 . ?0

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?]ono

? 1 non

31 000

3onnn

2 0 00 0

3 .30

? .P6

2 .8 5

2 • P 5

4 .00

4 .no

4.00

4.27

4.?7

4 . on

6 . ? ft-0

6 .04-0

7.07-0

0 .00-0

P .73-1

1 6.6P-0

1 6.79-0

1 ft . 1 8-0

1 5000

I 5nnn

16000

1 ?non

] 2 00 0

l^noo

PROD COSTS

X PLANT 1-AGE 1

OTY-GPU
A VC

forecast
pc t error

X PLANT 2-ACiF
OT Y-GRL)

A VC

FORECAST
PC T ERROR

Y PLANT 1-AGE 1

OTY-GRD
A VC

forecast

PC T EPROR

INVENTORY CARRJFO FORWARD
X STO-GRD
X DLX-ORO
X CUST/UMT

Y STD-GRO

Y COS T/ UN IT

1 pnnn-o

1 9000-0

2 1 000-0

1 pono-o

6.2ft

6 .04

7.07

ft .3 1

ft . 50

6.35

6.50

ft . 1 5

-26.12

-4 . ftft

ft .77

2 .ftO

1 9000- 1

i Qono- 1

ft .73

9.13

9.50

ft .70

-ft . 10

4.94

31000-0

31 000-0

35000-0

30000-0

16.6R

1 6.79

19.5ft

17.50

1 ft . 50

16.70

17.50

17.00

-9.ft3

.01

n . ft 9

3.47

797

2«1 2

7240

1 2 574

.53

.89

1 .*?

49?

^5ft4

? .4?

2.71

£5 w

ILLUSTRATION 3. CONTINUED

ending inventory

X SID-GRD

iqnon-o

1 q7P7-o

73817-0

7 6? 6 0-0

X DLX-GRO

0-0

n-n

l onnn- i

3i one- 1

Y STU-GRD

31 nno-0

3 ionn-n

354P7-0

33 5 «6-n

cash

-1 1 735Q

666395

631 3H8

7 5 6 A 0

FORECAST

700000

3 5 noon

PC T F RR DR

-) 56.18

733.20

115.69

-78 .39

SECURITIES

700000

500000

RFT FARMINGS

-37onnn

33876

3 A 7 37 F

567 ion

NET FARM X

-1 3nnno

1079F0

131^77

-36866

FORECAST X

■ -130000

5^000

98 5 60

700000

PC T FwRUR

103 .70

33.40

-1 1« .67

NFT FARM Y

- ] oonnn

455945

51 4547

6 6 OP 0 5

E U W F C A S T

-3 onnno

3o?nno

a snnnn

670000

PCT FRRUR

50.Q8

1 4 . 3 a

-IQ. 36

CURMT RATIO

2.F5

9.1 F

3.6 8

6.10

MU I

-10.67

9.1 F

5.00

7 .85

********* AREA 7 IFEC)

DFLFTEH REPORT

********* AREA 3 (KRAZ JL)

DELETED PEPU&T

********* HUME OFFJCE

PARTIAL REPORT

MKT RFSFAPCw

ITFF 1

I T F 7

JTFM 3

MAXIMUM PROOUCIRLF GRADF

product X

PRODUCT Y

HF.n PROD x

FOoon

60000

foooo

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80000

8 0 00 0

Rf,l> PRIin Y

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1 70000

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ao non

60000

n iv i n ends

RFT FARM JNGS ( CONSUL )

-71 51 61

— P 5 76 RR

- 3 4 H PPO

39*594?

857566

HU H CONSUL )

-1.07

- 1 .OQ

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5.50

7.38

3 .87

FORECAST

-3.00

-7.05

-° . M)

3 .90

6.10

6 . 05

kct Frrur

FA ,33

AF.H 3

1 P.36

M .0 3

70 ,9R

-36 .03

AVG FURFCAST ERROR

UNIT SALES

17.56

in .85

-5 .Qg

I.imJT VAR COST

-15.71

-A .35

-6.10

7 .66

NET EAR|\< OPS

40 .37

19.85

-15 .6Q

CASH

171.75

-160.38

-1 53.53

90.65

75 .49

-60. IQ

EFFICIENCY h FA SI IP F SUMMARY - QUARTER 6

CASH/ SAL

SUP CRP/

SAL FS

1NVT COST /SALES

MFT FARN/SAI.FS

ro i

TEAM

U/r.i RANK

u/n

RANK

n/p

RANK

n/n RANK

n/n dank

11.57

.63

• 46

79.06

8.85

IE. 69

3.77

37 .1 8

3.87

3.8 5

.34

1 . 51

73.04

6.86

76. QO

.1 1.8

61 .56

8 .05

74.68

1 . 31

35.56

P.PO

4.83

6. 14

4.58

73.53

6 .76

17.38

.67

48.50

17.71

17.67

.9°

3 9.67

8 .85

16.38

.91

36 .54

8.5?

ILLUSTRATION 3. CUNT1NUED

STK OUT /OPPllR

C£ A FROM

OPT I N

tfam

O/U

RANK

o/n

RANK

40.00

2 6.98

42.86

7.18

28.57

5.27

16.67

2.60

41 .67

1 6.60

20.00

78.94

11.11

18.45

38.50

37.^1

37.50

15.60

AVFRAGF FOR fcC AS T FRRUR SUMMARY - OllARTFR 6

UNIT SAIFS

UNIT VAR

COST

Nb T FARN

nps

T F Am

M/ll FRRUR

RANK

0/0 FRRUR

RANK

U/(l FORnR

RANK

19. 6

14.7

10.7

-6.0

2.5

-1 5.7

1 3.1

3.9

32.0

2.5

6.8

36.4

24.4

3.9

39.7

26.7

. 3

52.6

14.4

5.4

66.4

15.7

2.7

38.9

1 6.2

3.6

70. 1

A RF A CASH

H.n. CASH

ROI

TFAf*

O/U FRRUR

RANK

0/0 FRRUR

RANK

O/U FPROR

RANK

22.8

2.5

-5.6

-90.7

5.9

-36.0

69.9

6.8

-31.5

43.2

1 . 1

10.3

13.3

9.0

9.6

85.8

8.3

-8.1

8.9

9.3

4.6

103.2

6.6

- 10.6

19.5

5.9

5.1

;hest

N n .

PL A l

NTS

— -SI

rOCKClUT

S--

PATENT

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b FO

T F An

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1 3

—

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— —

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2 2

—

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—

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# =

PENALIZED

STOCK (IllT ,

UNPENAL JZEO

STOCK (JUT, -

■ =

STOCKOUT

SUARF

FFC

TEAM

12.6

17.9

14.2

12.6

18.5

7.4

8.4

11.8

6. 1

7.2

21.4

8.6

13.1

7.9

9.6

11.3

9.6

8.1

9.9

15.2

12.9

1 6.0

12.7

8.8

14.9

lo.o

8.1

19.7

12.3

1 5.6

7.1

10.0

9.2

8 R

AR F A

PFRCENT

ROI

FEC

13.3

32.5

5.7

12.1

20.8

9.8

2.3

5.2

3.7

39.7

22.9

4.7

5.1

7 .2

12.(5

9.4

10.4

3.3

23.0

23.8

5.5

12.2

1 6 .8

5.3

4.0

11.0

10.3

14.2

14.7

7 .7

8.0

12.0

8 .5

9.1

3 .?

ILLUSTRATION 4. Sample Peer Analysis Form

CONFIDENTIAL

Your Nome

GROUP ANALYSIS
Company (0)_

(Name)

You are assured chat all data on this sheet will be held In strict confidence.

List each member of your company, Including yourself. For each of the characteristics
listed, rate each member including yourself, on a 4.0 scale (2.0 ■ C)

Names In Slanted Columns \ \ \ \

Attendance at Team and functional meetings \

Completion of taaks delegated to Individual

Quality of work done by Individual on delegated tasks

Frequency of Ideas

Value of ideas

Ability to plan ahead

Use of analytic techniques

Ability to see and analyze other jpolnta of view

Carrying lair share of company* s work load

:o.

Overall value to company

ERLC

percentage rating of each team in each performance criterion by dividing thr
aeount attained in each by the aaount attained by the base teae.

5. Calculate a coeposite percentage for each teas and grade according to a pre-
established basis such as 90% - A, 80% 3 B, 70% * C, etc.

An additional 25 percent of the total grade is allocated to Individual performance of team
members. Except by subjective evaluation, it is difficult for the instructor to determine
whether each member of a team is carrying his "fair share1* of the load. Therefore, a portion of
the total grade is allocated to individual performance of team members, and it is basically
detrained by the studer.ts, themselves. Utilizing a standardized grading fora (see Illustraiton
4) provided at the beginning of the semester,, each team member grades all team members on ten
aspects of individual performance at the end of the semester. This forces students to assess one
another as working members of a stall group. Students have accepted this grading responsibility
guite seriously, rewarding and penalizing according to contribution or lack thereof,
respectively* The remaining 35 percent of the grade is allocated to traditional 0 quizzes and
examinations over course material.

fi esul ts - Discussion

At the 197 1 Conference nn Computers in the Or^rgradua te Curricula, Heyers[ 3 ] presented a
paper entitled, "We Don't Know What We Are Doing. " His basic theme was that we need to measure
more objectively the gains, if any, resulting from the use of computers in the undergraduate
curricula. I heartily agree with his theme and am sorry to note that we have not done any
systematic objective measurement of the gains (or losses), especially when related to costs
resulting from the introduction of the integrative core. Therefore, I think it important to note
the sub-heading title. Results - Discussion, instead of the more popular title. Conclusion.

The integrative core at Indiana University is not "new" in terms of subject matter. Rather,
it is the traditional business material wrapped in what we think is a more attractive package.
The expressed interest of students has been very high when compared with the prior curriculum.
The quality of the students' educational experience has been enhanced by the obvious integration
of courses. The Simulation course literally forces the student to pull things together. The
students know the four courses are interrelated by program design. Many of their classroom
comments and questions are related to work from one or more of the other core courses. The
content of the students' educational experience is enhanced by the presentation of traditional
theory within a framework of practical application. Students see how much techniques as cost-
volume-profit analysis, capital budgeting, "keep-out" pricing, etc. are utilized by a business
firm. They learr about the usefulness of theory in an environment substantially of their own
making. They also learn about the limitations and difficulties of trying to apply theory wh^n
other things seldom remain so conveniently ceteris paribus* Th* advantage of continually forcing
the transfer of theory into practice seems obvious to me.

"Poorer" students appear more motivated in the integrative core environment. Team
activities provide the framework for additional learning outside the classroom. Students are
willing to ask teammates about particular problem areas (and in the process implicitly admit
their lack of understanding) ; whereas, they will often not ask the instructor for assistance.
That overall understanding is increased and, at least, partially retained does not seem such a
rash subjective conclusion to make.

At least two objective conclusions can be made. First, considerable duplication in the
curriculum was eliminated. This resulted from faculty interaction aimed at development oi the
integrative core. It is interesting and sometimes embarrassing to find the same concept aeing
taught in several different courses. Hopefully, the elimination of duplication has freed time
for the introduction of other important material previously foregone. The second conclusion
which may seem trivial in retrospect, but certainly was not in the beginning, is that it is
physically possible to offer the integrative core concept. The obvious question is, "What are
the costs?" Administrative, computer and faculty costs are involved. The administrative cost
involved with strictly enforcing the prerequisites and arranging student and class schedules so
as to provide team integrity varies according to the routine presently in the system but
should rot be overlooked. Computer costs for the Simulation course vary directly with the number
of teams and the quarters to be simulated; however, a liberal estimate is two minutes of CDC
6500 central processor time for processing and analysis of one quarter of simulated operations
for a maximum of 25 teams. Central memory requirements are 1.20,000 words of core for each
program Both programs are already overlaid extensively; therefore, the stated core requirements
ace minimal. Because most University computer centers operate "funny money" accounts, it is
difficult to attach "real”dollar costs, but they are quite modest. The major cost is in terms of
human resources. In order for the core to work, periodic coordination of individual course
materials and development of integrative assignments must be accomplished* Due to the unusual
amount of work involved in the Simulation course, the instructors are given double teaching load
credit for each section of the course that they teach. In addition, two or three graduate

assistants foe each set of 25 teams ace needed to administer INTOP. One assistant is generally
responsible for handling computer processing and the second is responsible for editing an
industry organ that is a regular part of th^ output provided. In addition# the editor assists
the instructors in evaluating team perforaance since aany aggregate evaluations appear in the
organ in one fora or another, for the Simulation course, limited econoaies of scale exist with
increasing naabers of students.

Student reaction has been extremely favorable. The one aost often expressed dissatisfaction
is that coapletion of the core demands an unrealistic amount of time. The aaount of work and
study demanded is extensive, but it is so by design. The only way to survive in the Simulation
course is to divide and delegate the workload. There siaply is not tine for one student to carry
the entire burden; thus, ha is forced to pat faith and confidence in the reconnendat ions and
analyses of fellow tean members concerning their particular areas of operation. 1 have watched
teaas advance fron last place (by practically any criterion of measurement) to first place
siaply as a result of a structural reorganization. What better way exists for teaching such
concepts?

Tha future

To date, the assessment by the faculty of the integrative core has been extremely
fav Table. However, the faculty believes that aany potential advantages of the concept are yet
to bo exploited. The challenge is to create more meaningful assignments in each of the
functional areas utilizing the simulation output. 1 believe there is practically no end to the
integrative problems and assignments that may be developed.

ACKNOWLEDGE RE NTS

The author cannot possibly emphasize enough the fact that the curriculum program described
herein was conceived and developed by the faculty at the mother campus, Bloomington, and
especially by Professor Panscher, chairman of the undergraduate program. Also, Professor
Thorelli, INTOP9s primary designer has provided much of the motivation for development of
specific course materials. The author9 s experience with the undergraduate core program results
from his responsibility for teaching the Simulation course at the port Wayne Campus of Indiana
University and from the excellent interaction which occurs among the other similarly responsible
business professors at the seven campuses and himself. Some personal flairs described at the
course presentation level and some of the reactions to the core are those of the author.

REFERENCES

1. Chamberlain, Neil W. The Firm: flicro-Econoiic planning and Action, New York: HcGraw-Hill

Book Company, 1962, pp. 57-65. *

2. Greenlaw, Paul S. , L. W. Herron and R. W. Rawdon, Business Simulation in Industrial and

University Education. Englewood Cliffs: Prentice-Hall, 1962.

3. rteyers, Edmund D. , Jr., "We Don't Know What We Are Doing," Conference on Computers in the

Undergraduate Curricula. Dartmouth College, 1971.

4. Panscher, william G., "The Four Course Integrative Core," Unpublished paper, 1969.

5. Smead, Raymond J. , and Rodney W. Aldrich, Intop Analysis Program, Unpublished manual,

Indiana School of Business, 1971.

6. Thorelli, Hans B. , and Robert T. Graves, International Operations Simulation, New York:

The Free Press, 1964.

7. Thorelli, Hans B. , R. L. Graves and L. T. Howells, INTOP Player >s Manual. New Tork: The

Free Press, 1963.

8. Thorelli, Hans B. , INT3P (2nd. edition), Indiana Readings in Business #76, Indiana

University, 1972.

9. Welsch, Glenn A., Budgeting: Profit Planning and Control (3rd. edition), Englewood Cliffs:

Prentice-Hall, 1971.

STRUCTURE by Steve Jaroch

Problem: Continuous line design, offset on the X, Y , and X/Y values

ERLC

THE TIBE-SflAlIIS COHP0TBR AID I ITRRBEDI ATX ACCOOITIIG

Elbert B. Greynolds, Jr.
Georgia State University
Atlanta, Georgia 30303
Telephone: (104) 658-2882

Daring 1970 at Georgia state University, ve investigated the integration of a tine-sharing
coapater systea into selected undergraduate accounting courses. Since work of this nature had
been perforaed in introductory accounting, accounting-systens and auditing, ve selected the
interaediate accounting and cost accounting courses for onr study.

dost of the applications discussed in the accounting literature require "batch processing"
coapater systeas as equlpaent. As an illustration, consider the excellent introductory
accounting prograa library and text naterial developed by Vilbur P. Pillsbury, which he
discussed at the 1971 conference at Dartnouth College[ 1 ]. His naterial was designed prinarlly
for Introductory accounting and a batch processing conputer systea. However, we wanted to work
with advanced accounting courses and a tine-sharing conputer systea.

tfe were anxious to exploit the flexibility offered by an interactive conputer systea. The
concept of having the student use the conputer as an analysis tool as well as a problea solver
in accounting excited us.

Objective

Our objective was to integrate a tine-sharing coapater systea in selected accounting
courses. There were two qualifications in our objective. First, the nethod of integration should
allow initial i nplenen tatlon in the courses without causing significant changes in their
structures, second, the conputer should Initially be a suppleaental aid in the courses.

Scope and Liajtatigns

naterial was developed for cost accounting and interaediate accouatlng courses, but testing
was restricted to the interaediate area. Ve chose the interaediate courses for several reasons.
First, work of this nature is needed in the area since conputer applications in interaediate are
not as apparent as in cost accounting. Host of the cost applications are readily recognized as
being valuable student aids.

The coapater equlpaent used in the study was restricted to tlae-sharing coapater systeas
with reaote terainal capability. Excluded fron use in the study were batch processing systeas
and prograaning languages such as POBTIAI and COBOL. Because ve wanted to keep the project oa aa
eleaentary level, the prograaning language BASIC was used for all prograas. The alnpllclty of
BASIC and its vide usage on other systeas were key reasons for its selection.

All prograas were developed and tested using the Georgia state RCA Spectra 70, Hodel 46,
Tine-sharing Systea. Students had access to approxiaately twenty terainals during the study.

RESEARCH

EE23EM hk &I2EI

The first step in oar study was obtaining a suitable tlae-sharing prograa library of
applications. Ve investigated the tlae-shariag prograas available to educational institutions. A
review of these prograas, however, revealed substantial duplication. Host of the prograas were
designed for applications in statistical, natheaatical and other non-business areas. The
financial prograas available were oriented toward "Finance" courses and generally were not
suitable for our study. Vhen ve narrowed the review to progress written in "BASIC," the deficit
in financial accounting prograas was apparent. As a result, ve decided to develop the accounting
tlae-sharing library at Georgia State.

Develrppaqnt of Prograa Library

The financial accounting library was developed using several guidelines. First,
representative accounting topics were selected with as little duplication as possible of
existing prograas. Second, the prograas were written so that students could use then as problea
solvers or analysis aids. He wanted to release the student fron the burden of lengthy

i ;

computational problems as well as allowing him the luxary of concentrating om the analysis of
accounting problems rather than their solution.

The programs for the accounting library were evaluated according to six standards described
below. The first four were primarily satisfied by propmr program design, and classroom testing
satisfied the last two standards.

First, the material for which programs are developed should be contained in currant
accounting textbooks. Second, tha programs should be capable of utilization in connection with a
representative number of problems contained in current accounting textbooks. As a result, a
reasonable reduction in computation time should result. Third, program terminology shoald ba
consistent with accepted accounting terminology. Fourth, the programs should be referrenced to
specific accounting textbooks used in financial accounting courses. Change of a course textbook
shoald require only minor changes, if any, in the program. Fifth, tha programs should be easily
applied by the students. Sixth, the programs shoald be reasonably free of errors.

Topic Selection

In selecting accounting topics for inclusion in the program library, we examiaed
representative current accounting textbooks within the following classifications: Cost
Accounting, Intermediate Accounting and Advanced Accounting.

Because the programs were to be tested at Georgia state University, emphasis was given to
the textbooks used in the various accounting courses at state. The topics we selected for
programming are also in other standard accounting textbooks. This selection does not exhaust
all possible applications for program development; rather, the topics were chosen to illustrate
the integration of a time-sharing computer system and accounting courses.

The accounting topics selected and programmed for the time-sharing library are:

Financial Statements

Depreciation

a. Common depreciation methods

Financial Analysis

b. Annuity depreciation

Ratio analysis

c# taking fund depreciation

Break-even analysis

C m

Cash budgets

10.

Coinsurance Calculations

Contribution margin analysis

Variance analysis

11.

Goodwill

1. Direct labor and material

2. Overhead

12.

Leasehold Amortization

13.

Installment Loans

Capital Budgeting

14.

pension Past Service cost Amortization

Present value computation

Internal rate of return

15.

Bond Analysis

computation

a. Bond valuation and yield

c .

General purpose capital

b. Compound Interest amortization of

budgeting model

premium or discount

c. Gain or loss on bond redemption

d. Entries for purchases or sale of

boad between interest dates

Compound Interest Calculations

16.

Serial Bonds

Cost

Accounting

a. serial boad valuation

Process costing

b. Amortisation of preaiua or discount

Reciprocal

1. Straight line

2. Compound-interest

Bank

Reconciliation

17.

Sinking Fuads

a. Ordinary fund

b. Fund for serial bonds

Average Due Date of Account

Inventory Valuation

Lover of cost or market

; 18-

Stocks

Common inventory valuation

a. stock right valuation

methods

b. Preferred and coiaon stock

Retail inventory methods

dividends

The eighteen topics are contained la forty programs developed for the study. He also
selected eight existing mathematical programs for Inclusion la the library.

Be wrote spaclal instructions so tha ataduta coall use the progrm with a aiaiaaa of
assistance. The prograa InstrQctloaa gaaarally followed this format:

1. Program aaae

2. Parpoaa of program

3. Befaraaca to mpeciflc accomntlmg textbook a

4. Pormatm for data iapmt

5. Samplm problmm coataiaed im textbook

To facilitate student a sage of tha library, wa coapiled tka prograa lnatructioaa in a
aaaual: Uje aiUll SZtitl ABBlifilligH il iSSIUtiUt 2 )• mill alao coataiaa appropriate
instructions for osiag the tlaa-ahariag ayatea and teraiaala.

lifesan SzzlMilsB

As prewioasly noted, four of our six library avalnatloa criteria wars satisfied by proper
prograa and instruction design. The evaluation of tha raaainiag critaria regairad atudaot
response, which was obtained by claaarooa testing, fa basically waatad to find out if the
prograas ware error free and if they could aaaily be used by stadaata. Be also sought their
opinion on the value of tha prograaa.

For our test, four lataraediate Accounting classaa taught by three iaatructora were
selected. This test was conducted during tha 1970 Suaaar quarter. At Georgia State, lataraediate
Accounting ia a two quarter courae. Our taat group ieclnded three firat quartar claasaa and one
second quarter class. For evaluation purposes, va dividad the claaaaa into three groups*-!, B
and C. Group A, a firat and aacoad quarter class ware given technical assistance ia using the
library. The other two classes. Groups • and C raceivad no technical assistance. Tha coaputer
background of the instructors varied. Tha instructors of Groapa A and B had very little
experience while Group C*s instructor had axteaaive axperiaace with coaaarical syateaa.

Group A* s students were required to work a auaber of homework probleas using the accounting
library. The probleas were salactad froa a list we furnished to tha instructors.

The application of the prograaa in tha other two groups was different. Vhile student
questions concarning program usage in Group A were answered, the other two groups usad the
prograas on a "blind" basla. The instructors of Groups B and C racaived an explanation of the
project and a list of the problems, after which no further assistance was given. The studaats ia
these groups used the prograas oa a voluntary basis.

The purpose of assisting then differently was two-fold. First, if tha prograa instructions
vere sufficiently clear and the prograas wera ganarally frea of errora, the studanta ahould be
able to apply the prograas without assistance. Second, it was deairable to senae or aaasura
difference in response aaoag the groups.

gueg&ignnajre

A questionnaire was developad to obtain atudent opinion coacerniag eaaa of application,
reasonable freedoa froa errors, and usefulness of the prograas la problea solution. Be aade ao
atteapt to aeasure either student understanding of accounting or knowledge of tiaa-ahariag
systeas. The purpose of the survey was to dateraiae whether accounting studaats could uae thesa
prograas in their courses. As a result, tha evaluation is qualitative rathar than quantitative.

The questionnaire given to the students at tha end of tha quarter coataiaed thirty
questions. The questionnaire results are suamarized below, aad wa will supply datalls to
interested parties.

The students' responses Indicated that thay could uaa tha prograaa without difficulty aad
that the prograas were generally error free. Thay lndicatad that ualag tha coaputer in the
accounting courses was beneficial to them, aad that it should ba coatlnuad. Thay also lndicatad
that tlae was saved in working homework problems.

Because the prograas vere latendad as a supplement to stuiant learning and classrooa
teaching, the student aust know the fuadamental accounting techniques 1 corporated in each
problea. This assumption was supported by the studenta. They indicated that the uae of the
prograas did not initially teach then the accounting techalquaa, but rainforcad their
understanding through analysis. The overwhelming majority of all groups Indicated they would ba
willing to use the tiae-sharing computer in other courses and would ba willing to learn BASIC.

The aajor coaplalnt by the students concerned teralaal availability. They felt that aore
teralnals should be provided.

63 74

PROGRAM NAME--DEP8

PURPOSE I

THIS PROGRAM COMPUTES DEPRECIATION BY THE SINKING
METHOD AND THE ANNUITY METHOD. FOR DETAILS SEE PAGES
636 TO 639 IN INTERMEDIATE ACCOUNTING BY WELSCH
ZLATKOVICH AND WHITE.

INSTRUCTIONS:

CALL UP THE PROGRAM AND TYPE RUN. DATA LINE
STATEMENTS ARE NOT REQUIRED FOR THIS PROGRAM.

THE INPUT VARIABLES ARE:

A-C0ST OF ASSET.

B-SALVAGE VALUE OF ASSET.

C-LIFE OF ASSET IN YEARS.

D- INTEREST RATE.

SAMPLE PROBLEM:

THIS PROBLEM IS TAKEN FROM THE TEXT QUOTED ABOVE ON
PAGE 637-

COST a SIOO
SCRAP VALUE = SIO
YEARS OF LIFE = 3
INTEREST RATE = 52

OLD

OLD PROGRAM NAME--DEPS

READY

♦RUN

ENTER COST CA>» SALVAGE <R>. YEARSCC) AND INTEREST
RATE CD). A»B»C»D?I09» 10.3. .05

BOOK VALUE YEAR 0 = JOO
SALVAGE IS 10

INTEREST RATE IS .05

LIFE IS 3 YEARS

DO YOU WANT ANNUITY PRINTED: YES (I). NO CO)
?1

♦♦♦ANNUITY METHOD OF DEPRECIATION ♦♦♦

PERIODS

INTEREST

ANNUAL

CREDIT T0

DEP-

ACCUMULATED

I NVESTMENT EXPENSE

DEP.

33.5493

28.5493

3.57254

33.5493

29.9767

2.0737

33.5493

31.4755

TOTAL

10*6462

100*648

90*0015

00 Y0U WANT
?t

SINKING FUND

METHOD! YES ( 1 )#N0(0)

BOOK

VALUE OF
ASSET

7J .4508
41.4741
9.99854

FIGURE 1 . Program Name DEP8

♦ ♦♦SINKING FUND METHOD 0F DEPRECI ATI 0N^ +

ASSUMED

INTEREST

B00K

DEPOSIT

VALUE

EACH

FUND

DEP.

ACCUM.

PERIOD

BALANCE

EXPENSE

DEP*

ASSET

28. 5493

28.5493

28*5493

71.4508

28.5493

1 .42746

29.9767

58. 526

41*474

28.5493

2.9263

31 .4756

90.001 5

9.99849

T0TAL

85.6478

4.35376

90.0015

FIGURE

1. Continued

PROGRAM NAME— COINSUR
PURPOSE!

T0 C0MPUTE THE MAXIMUM INDEMNITY F0R A BLANKET PfLICY
0R WHEN A C0 INSURANCE CLAUSE IS INCLUDED IN A P0LICY
T0 C0MPUTE THE MAXIMUM INDEMNITY F0R 0NE 0R SEVERAL
INSURERS. F0R A DISCUSSI0N 0F THE C0MPUT AT 1 0N AL DETAILS
SEE INTERMEDIATE ACCOUNTING BY WELSCH* ZLATK0VICH AND
WHITE* PAGES 366 T0 369.

INSTRUCTIONS!

DATA LINE INPUT IS REQUIRED FOR THIS PROGRAM. THE
GENERAL FORMAT ISt

100 DATA N»P(1)»P<2)»...»P<N)

200 DATA N*R(1)*R(2)*...*R(N)

N-NUMBER OF POLICIES FFOR BOTH DATA LINES.

P(I ) -AMOUNT OF INSURANCE CARRIED (FACE VALUE) FOR
EACH P0L ICY •

R( I ) -CO- INSURANCE RATE FOR EACH POLICY IN LINE 100.

IF NONE OF THE POLICIES HAVE COINSURANCE CLAUSES*

THEN DO NOT MAKE AN ENTRY IN DATA LINE 200* LEAVE IT BLANK.

IF THE POLICIES DO HAVE COINSURANCE
CLAUSES* THEN A RATE MUST BE ENTERED FOR EACH POLICY EVEN
IF ONE OF THE POLICIES DOES NOT HAVE A CLAUSE* IN SUCH A
SITUATION ENTER A RATE OF 0.

USING THE FIRST EXAMPLE ON PAGES 368-69 OF THE TEXT* THE DATA
LINES WOULD BE I

100 DATA 4*10000*25000*40000*5000
RUN

USING THE SECOND EXAMPLE ON PA6E 369* THE DATA LINES
WOULD BE!

100 DATA 4*10000*25000*40000*5000
200 DATA 4* .9* .9* .9* .9

FIGURE 2. Program Name COINSUR

IF THE COINSURANCE RATES VARIED* THE DATA LINES WOULD
BE*

IOO DATA 4* 10000*25000*40000*5000
200 DATA 4*0* .75* .8* .90

SAMPLE PROBLEMS

THE DATA TOR THIS ILLUSTRATION IS TAKEN FROM THE
EXAMPLES FOR DATA LINE ENTRIES ABOVE.

ALL USER SUPPLIED I NT 0RMATI ON IS UNDERLINED.

OLD

ALP PROGRAM NAME--C0 I NSUR
READY’

- 1 0 o DATA 4* 10000* 2 5 000*4 0 0 00* 5000

ENTiX~i:AIR MARKET VALUE OF INSURED ASSETS (M>* AND
AHO'.XT OF LOSS CL). M*L?

? I CC'O'.'A* 60000

CO- INSURANCE TABLE

POLICY

C0-INSUR.

I NSUR •

REQUIRED

NO.

CLAUSE

CARRIED

BY CLAUSE

0 %

10000

0 %

25000

0 ?>

40000

0 2

5000

TOTAL

80000

100 DATA A.* 1 0000> 25000*40000# 5000
*200 DATA 4> .9* • 9# • 9* • 9

*RUN

ENTER FAIR MARKET VALUE 0F insured assets CM># and
AM CUNT OF LOSS <L>. M,L?

? 1 00000# 60000

CO- INSURANCE

TABLE

POLICY

CO-INSUR.

INSUR.

REQUIRED

NO.

CLAUSE

CARRIED

BY CLAUSE

?0 Z

10000

90000

90 %

25000

90000

90 Z

40000

90000

TOTAL

90 Z

5000

80000

90000

FIGURE 2. Continued

MAXIMUM
COLLECT IDLE

7.500

18750

30000

3750

60000

MAXIMUM

COLLECTIBLE

6.666*67

16666.7

06666.7
3333.34
53333 • A

PR0GRAM NAME --PENSI ON

PURPOSE :

THIS PROGRAM COMPUTES THE ACCRUAL FACTOR# INTEREST
AND TOTAL PENSION COSTS AS WELL AS THE CASH CONTRIBUTION
AND BALANCE SHEET AMOUNT FOR PENSION PAST PERIODS
SERVICE COSTS.

REFERENCES

CONSULT INTERMEDIATE ACCOUNTING BY WELSCH#

ZLATK0V I C H AND WHITE PAGES 848 TO 890-

INSTRUCTIONS:

DATA LINE INPUT IS NOT REQUIRED FOR THIS
PROGRAM. TYPE RUN AND ANSWER THE INPUT QUESTIONS-
THE INPUT QUESTION VARIABLES ARE:

A = THE INITIAL ACCRUED ACTUARIAL LIABILITY OR
PAST SERVICE COST-

B = THE NUMBER OF YEARS THE PAST SERVICE COST HAS
BEEN ACCRUING.

C = THE NUMBER OF YEARS THE PAST SERVICE COST WILL
BE WRITTEN OFF OVER.

D = THE INTERVAL OF YEARS FOR THE PRINT OUT. FOR
EXAMPLE IF D = 5i THEN ONLY EVERY FIFTH YEAR
WILL BE PRINTED IN THE TABLE

R = THE INTEREST FACTOR FOR COMPUTING INTEREST.

SAMPLE PROBLEM:

8 YEARS AFTER ITS FORMATION# SMITH AND JONES CO.
DECIDED TO ADOPT A PENSION PLAN. THE ACTUARY DETERMINED
THAT THE INITIAL ACCRUED ACTUARIAL LIABILITY
FOR PAST SERVICE COST AMOUNTED TO $425#000-
USING A 4% RATE AND ASSUMING THAT THE PAST SERVICE
COST IS TO BE FUNDED IN 12 YEARS PREPARE
A TABLE FOR DETERMINING THE ENTRIES NECESSARY TO
RECORD THE PAST SERVICE COST. HAVE THE TABLE SHOW
EVERY OTHER YEAR •

OLD

OLD PROGRAM NAME--PENS I ON

READY

♦RUN

ENTER THE AMOUNT OF THE PAST SERVICE COST IN A.

ENTER THE NUMBER CF YEARS FOR THE ACCRUAL FACTOR IN B.
ENTER THE NUMBER OF YEARS IN THE WRITE eFF PERIOD IN C.
ENTER THE INTERVAL OF YEARS FOR PRINTOUT IN D.

ENTER THE EARNINGS RATE IN R AS A DECIMAL.

A#B#C#D#R

7425000# 8# 1 2 # 2# .04

FIGURE 3. Program Name PENSION

PENSION PAST PERIODS SERVICE COSTS

AMOUNT CHARGED TO PENSION EXPENSE

ACCRUAL

AMOUNT OF

PENSION

YEAR

FACTOR

INTEREST

COST

63124.4

63124 .4

713.587

63838

63 124 .4

2227.53

65351 .9

63124.4

3865.01

66969.3

63 124 .4

5 63 6. 1

68760.5

5026.74

5026. 74

1 741.69

1 741 . 69

CASH
AMORT.

45284. 7

45284.7

45284. 7

45284.7

BALANCE
SHEET AMT

1 7839. 7
36392.9

75755.4
1 18330

1 64378

85410. 5
-.847656

FIGURE 3. Continued

PROGRAM NAME--BD AMORT
PURPOSE:

THIS PROGRAM CALCULATES BOND AMORTIZATION BY
THE SCIENTIFIC METHOD AS DISCUSSED IN INTERMEDIATE
ACCOUNTING BY WELSCH# ZLATK0VI CH AND WHITE PAGES
665 TO 669. FOR MORE INFORMATION CONSULT THE
INTERMEDIATE TEXT.

INSTRUCTIONS:

CALL UP THE PROGRAM AND TYPE RUN. DATA LINE
STATEMENTS ARE NOT REQUIRED FOR THIS PROGRAM.

THE INPUT VARIABLES ARE:

A-NOMINAL INTEREST RATE# FACE RATE.

B-YIELD INTEREST RATE.

C- TOTAL PAR VALUE OF BONDS IN DOLLARS.

D-CARRYING VALUE OF BONDS# OR AMOUNT PAID FOR BONDS.
E-NUMBER OF YEARS TO MATURITY FROM PURCHASE DATE.
F-NUMBER OF MONTHS BETWEEN INTEREST PAYMENTS.

SAMPLE PROBLEM:

THIS PROBLEM IS FROM THE TEXT QUOTED ABOVE ON
PAGE 665.

BONDS PURCHASED ON APRIL# 1# 1970 WITH A PAR VALUE OF
S10#000. THE BONDS MATURE ON APRIL 1# 1973, AND

THE NOMINAL INTEREST OF 5% IS PAID EVERY SIX MONTHS
BEGINNING WITH OCTOBER 1#!970. THE PURCHASE PRICE OF
THE BONDS WAS $!0#230.07# AND THE YIELD WAS 4%

ON AN ANNUAL BASIS.

OLD

OLD PROGRAM NAME- - B0AM3RT

READY

*RUN

NOMINAL INTEREST RATE (A)# YIELDCB), TOTAL PAR
OF BONDS <C># CARRYING VALUE OF BONDS CD)# NUMBER
OF YEARS TO MATURITY (E)# MONTHS PER INTEREST
PAYMENT <F>. A#B#C#D#E#F
?. 0 5# .0 4# 1 0000# 1 0280.07# 3# 6

FIGURE 4. Program Name BDAMORT

BAND PREMIUM ( D I 2C0UNT ) AMORTIZED DY SCIENTIFIC METHOD

CONSTANT

0RGINAL

CASH PAYMENT (RECEIPT) 250
CARRYING VALUE OF BOND 1 02 SO- 1

PERIODS

CASH

RECEIPT

(PAYMENT)

INTEREST
INCOME
( EXPENSE)

BOND

PREMIUM

(DISCOUNT)

INVESTMENT

CARRYING

VALUE

2 50

205.601

44.39R7

10235.7

2 50

204.713

45-2360

10190.4

2 50

203. 002

46. 1925

101*4.2

2 50

202. 884

47.1163

10097. 1

52 SO

201.941

43 • 0587

10049

250

200. 98

49.0199

10000

TOTALS 1500

1219-93

250.073

RIJN

NOMINAL
GF BONDS
GF YEARS
PAYMENT
?.0S# . 06

INTEREST RATE (A)# Y I EL D 03 ) # TOTAL
(C), CARRYING VALUE OF BONDS (D>,
Tv MATURITY (E), MONTHS PER INTER
(F). A,3#C,n#E*F
# 1 0000# 9729. 1 4# 3# 6

PAP

NUMBER

EST

BOND PREMIUM (DISCOUNT) AMORT 1 7

ED r)Y SCIENTIFIC

METHOD

CONSTANT
ORG IN AI-

CASH PAYMENT (RECEIPT) 250

carrying value or bond 9729.14

DER 1 0D$

CASH

RECEIPT

(PAYMENT)

INTEREST

INCOME

(EXPENSE)

BOND

PREMIUM

(DISCOUNT)

INVESTMENT

CARRYING

VALUE

250

291.874

-41.874

9771.01

250

293. 13

-43. 1301

981 4. 14

250

£94. 424

-44. 4241

9858.56

250

295.757

-45.7569

990*,. 32

250

297. 13

-47. 1294

9951.45

250

298. 543

-4S. 5432

10000

TOTALS 1500

1770.36

-270.858

FIGURE 4. Continued

At the clone of the Sonner quarter, the three teat groupa* profeaaora discussed the student
evaluation of the project. Their coaaeata aapported the reapoaaea of the students. They
considered the prograa library to he a valuable tool la the clasnroon, easily applied,
reasonably free of errors, and capable of ntilizatioa with current textbooks. They agreed that
the progress were successfully introdeced iato their courses without causing significant
changes.

No appreciable difference in student responses was found within the furious groups. The
three groups all had siailar questionnaire results, ewes though there were differences in the
coaputer experience of instructors and in the sethod of applying the progress.

Conclusions

After efaluation of student and teacher responses and the tine-sharing library, we
considered the objective of the study to be achieved. He successfully desosstrated the
integration of a tine-sharing coaputer systes with iateraediate accounting courses. «e did this
on a practical basis, students and teachers are not required to possess progressing experience,
nor are significant changes in the coureea required.

(e are heartened by the students* response toward using the coaputer in their clannen. This
is an intangible result, which we beliewe to be ieportant. They appeared to display iscreaset
interest in accounting coaputer applications, and apparently are nore confortable with the
coaputer after usinq the library.

By using our approach, the coaputer can be introduced into iateraediate accounting with
•ini sal disruption. Ve beliewe that the sane results an abowe could be obtained in cost
accounting courses if the appropriate pragmas were tested and ewaluated.

Soee connents on the resources necennary for the dewelopsent of a library ninilar to ourn
are appropriate at this point. The prograas in our library were deweloped by us in six aonthn on
a part-tiee basis. Ve had full-tine across to one teletypewriter terminal.

Ve will be happy to supply copies of the progress to interested individual users upon
request. Just send us a nagnetic tape anf the appropriate npeclf lcatlons for your synter. Copies
of the instruction annual for the library are available fron the Georgia state university
Bookstore.

The prograe instructions were prepared ening the coaputer. The instruction! were stored in
programs which allowed us to nodify then when necessary. This also explains why all upper-cane
printing is used in the exaaples. The exanplen we selected for illustration are taken fron the
instruction eac^al. Because of the length of none instructions, we have selected short exaaples.

The accounting areas illustrated are:

1. Depreciation:

2. Insurance:

3. Pensions

4. Bonds

DBP9— Sinking Fond and Annuity Depreciation

COllSUt— Co- insurance Calculation

PEVSXOl— Vrite-of f of past service costs

BDABOBT — Bond amortisation by the
coapound-iaterest nethod

The text referred to in the instruction! is Intereedlnte Accoyptjig by Velsch, tlatkovlch,
and Vhite, published by Bichard D. Irwin. This was the intermediate text used by the school
during the study.

REMOTE TIME-SHARING FOB EDUCATION III BUSINESS PLANNING AND CONTROL

Harley H. Courtney
The University of Texas at Arlington
Arlington, Texas 76010
Telephone: (8 17) 273-3481

Introduction

Business planning and control courses have traditionally suffered from an inability to
coanumcate the discipline to students in an adequate fashion. Typically the student is told how
business firas perform the planning and control function, and soae exercises a:& solved which
illustrate the tools available to corporate planners. But the assigned exercises are usually so
siaple as to preclude any substantive understanding of the total aanageaeut process, and
consequently, are an inadequate representation of the merits and liaitations of the tools
utilized. Moreover, the simplistic nature of the exercises precludes the acquisition of any
significant grasp of the behavioral aspects of the decision process or of the heuristic nature
of business aanageaent.

But the appearance of tine-shared coaputer terninal facilities on aany university campuses
proaises the possibility of substantive courses in business planning and control. The facilities
will free students froa the coapu tational constraints presently existing and will thereby permit
the realistic illustration of aatheaatical nodels as well as the behavioral dinensions ot the
discipline.

In 1970, The University of Texas at Arlington offered a new course titled "Nanageuent
Planning and Control," required of all accounting aajors. The course has been popular with
the* and has attracted nuaerous students froa other business disciplines, notably finance and
aanageaent. Upon the initial offering of the course, atteapts were aade to utilize a batch-
processing coaputer facility on campus. This step was of soae benefit since coaplex cases having
predetermined solution paths could be analyzed. But severe probleas remained. Most planning and
control probleas did not appear to have solution paths which could be aapped in advance of the
data analysis. Multiple runs of data were possible, but the turnaround tiae ranged froa hours to
days. This is probably typical of aost caapus computer centers aiid effectively precludes any
significant nuaber of multiple runs. when one reaeabers that designers of CAI systems feel that
a response tiae of five seconds or less is necessary to aaintain student interest, it is easy to
understand why a batch systea is inefficient.

Not only were case analyses difficult froa the cob putational viewpoint, but the behavioral
and heuristic dimensions of aanageaent choice could only be alluded to by the instructor rather
than being illustrated and experienced by the student during the process of case analysis.

This latter problem is particularly acute in corporate planning and control courses since
they are both tool-oriented and integrative, utilizing accounting and statistics on the one
hand, and psychology and aanageaent organizational behavior on the other. In such an
environment, computational inadequacies result in the student being told how a task should be
accomplished, rather than being confronted with an illustration of the task and the opportunity
to participate in a reasonable facsimile of it.

The availability of tiae-sharsd computing has permitted this highly desirable relief froa
computational constraints at UT-Arlington. During the suaaer of 1970 the first tentative steps
were taken to integrate the use of tine-shared remote terminals into the instruction of business
planning and control, while the initial use was liaited so as to determine its feasibility and
instructional talue, rapid growth in use has occurrf At present, ail course instructors use
the facility <*od its use has spread froa one course topic to aost of the topics considered in
the course.

Applications of ^iae-Shared Computing

Initial applications of the tiae-shared terainal were relatively simple to inpleaent.
Nevertheless, the benefits were substantial. Two early uses were the solution of cost-voluae-
profit and capital budgeting cases by the use of canned prograas authored by the instructor.
These progi'as were interactive in nature such that students having no previous acquaintance
with the coaputer were able to utilize them with no instructions other than the steps involved
in signing-on, calling the prograas, and signing-off.

Exhibit 1, fur exaaple, illustrator the use of a simple capital budgeting problem. All
typing by the user in the exhibit is indented; all typing beginning at the left aargin was under
coaputer control. Thus the user typed the naae of the prograa - riPBUDGKT - and the terminal
response ua. to ar*k the user questions to which he responded by typing in the answer, lote t U it
the student cannot only solve pro' leas with unigue inpn s, but he can also perfora a sensitivity
analysis. The second example run in Exhibit 1 assuaes the construction of a commercial building
with relative certainty as to revenues since leaser* have already been signed, but uncertainty
regarding the final construction coai • Thus se veral possible tocal costs can be entered to
deternine the ssneitivity of net present value and payback to possible cost overruns.

Moving frj* this relatively siaple situation, a note conplex case was written which
required numerous decisions to be nade by the student while tie analyzed case data at the

coaputer terainal. When studying the topic of flexible budgeting the student learned fron

reading and lectures that budget allowances in businesses should be related to the levels of

activity currently being experienced by the fira. Moreover, to accomplish this one east divide

accounting costs catagories into fixed and variable coaponents, which requires the selection of
an activity aeasure to associate with each cost. This process of choosing an activity aeasura
involved ttoae logical and eapirical association of cost variances with the activity levels.

The case required that a flexible budget be prepared for the production department of a
manufacturer of beer augs. All information, including the problea description was stored in the
coaputer systea and called by the student. Be was given data for four production expenses and
four activity measures covering twelve accounting periods. Canned programs *or correlation and
regression were provided. These were interactive and instructions were provided on their use. A
plot program allowed the student to visually scan the relationships between independent
variables (activity measures) and dependent variables (expenses).

solution steps to the case included the selection of an appropriate activity measure for
each expense. Tb<± student was not only expected to utilize the statistical programs, but to also
consider whether the activity measures and expenses having the closest relationship could be
logically associated, given the nature of the production process. The following typical problems
encountered in practice were built into the data:

1. Pairing the activity aeasure and expense having the highest correlation

resulted in a material negative fixed cost being budgeted.

2. Pairing the activity aeasure and expense having the highest correlation

resulted in an immaterial negative fixed cost being budgeted.

3. An activity aeasure having a strong logical association with an expense

correlated poorly due to a single observation deviating significantly froa a
rather unifora pattern.

The student was instructed that there was no unique solution to the case, but rather each
student vat. to analyze the data and construct a flexible budget which he felt would be aost
useful for planning and control. Choices could be nade among the activity aeasures for each
expense and one could delete observations froa the accounting data (twelve periods provided) in
constructing the budget.

Many students, for exaaple, felt that ovenhours was a logical activity aeasure for
coke cost even though the correlation was relatively low as indicated in Exhibit 2. Their
judgment was validated when coke cost was plotted as a function of ovenhours (OVHBS) since it

was discovered that, il: one observation was excluded, a very high correlation existed. To

determine which observation of the twelve was the non-representative one, the student could
display the data by typing the index of the data (OVHBS and COKE) and then attempt to locate it
by inspection. A simpler approach illustrated in Exhibit 2 is to divide coke cost by ovenhours
and inspect tht unit cost figures, thus the fifth observation is easily distinguishable as the
non-representative one.

At this point the student could ask the instructor for an explanation of the unusual cost

which occurred in the fifth period. The answer given was that a rare malfunction occurred in

the coke burner, thus increasing coke consumption above noraal. Students then decided whether to
include or to exclude that observation from their budget.

Answers to situations of this kind can vary to illustrate various probleas which exist in
planning and control. Other possible causes of unusual costs include errors in recording
accounting transactions, disruptions in other parts of the production process which impacts on
the cost under consideration* irregular outlays which are expected and justifiable, and poor
control. The student aust decide whether to include such cost observations in his budget, and it
sof how to include thea.

C/iPffU ,

ENTER THF INVESTMENT OUT LA /

25000

ENTER THE ANNUAL CASH FLOWS, SPACING RRTWNEN AMOUNTS
0:

2500 4000 6000 850C r.OOT. 7S0O 4000 1070
ENTER THE INTEREST RATE
0:

THE NET PRESENT VALUE IS .$26 12.08
PAYBACK IS 4.47 YEARS.

CAPBUDGET

ENTER THE INVESTMENT OUTLAY

500000 550000 600000

ENTER THE ANNUAL CASH FLOWS. SPACING BETWEEN AMOUNTS
0:

50000 70000 70000 70000 70000 70000 70000 70000 80000 80000 80000 80000
ENTER THE INTEREST RATE
0:

.07

TRE NET PRESENT VALUE IS $57010.32 7010.32 "42989.68

PAYBACK IS 7.42 8.14 8.85 YEARS.

.EXHIBIT 1 : Illustration of the use of a capital budgeting model

nCSCRlPTIOfl

T nr'

The

student t.vnos the prop. nane
connutor asi:s for Input

COFP

ENTER TVr VALUES FCl: THE 7 NLLHST • , ' ■ ■ ;.r

The

name of the varlble Is typed

OVHFS

FHTFF THE ’'ALVES EOF ?"F DEPENDENT VA.EIADLF.

Sane two ste^s as above

COKE

Answer - correlation Is low

CO REFLATION IS n.7 53

^ S 0

The student calls for the plot program 15 40 plot COKE i/s ovilFS

3250 |

One observation at S3, 000 and about aoool

328 hours Is atypical I

2750 |

o 00

o o
o

To locate the atypical observation
the student computes the unit cost

Observation five Is about SI greater
than the others.

I o

25001 I |

300 320

340 360

c or. r ■

0.27795527/ s .

8.236311234

8.200564972

8.141643059

8.216 8 . c 6 f. 3 ;

8.158176944 8.14707R996

380

The correlation program Is run again
deleting data from period five.

Correlation Is satisfactory

mrr

EKTF.F 7."' VALVES FOP TVF. INDEPENDENT VARIABLE

□ :

11110111111 1 /OVB’pS
ENTER THE VALVES FOP THF DEPENDFE:' VAPIABT.F

11110111111 1 /COKE

0 OFF SI AT IP N IF 0.984

The regression pr in Is used to
separate costs Into fixed and
variable and to determine
tolerances for cost variances.

DEGRESS

THIS PFOGFAf CONFUTES VALVES (A AND P ) FOF SItIPLE
REGRESSION AFP IFF. STANDARD EPFOF.

FFTEF TFF VALUES FOF THF INDEPENDENT VAFIABLF.
fl:

11110111111 1 /OVHFS
FFTEF TFF VALUES FOF THF PFPFFDEKT VAFIABLE
□ :

11110111111 1/COKE

Fixed cost
Variable cost

Statistic for setting control Units

A IS i 137.287

F IS: 7.777

STANDARD FPPOF: 27.032

EXHIBIT 2 : Illustration of Stops in Plaxiblo Budget ng Case.

,$S

o o

Note in Exhibit 2 that the aechanical aspects of the analysis voce alaost effortless in
tha* the student did not have to enter the nuaerical data, but siaply typed the indm: (naae)
under which the data was stored. Horeover, the prograa which displayed the problea also
instructed hia in the deletion of unwanted data. The second run of the correlation prograa and
the regression prograa in Exhibit 2 illustrate that the fifth observation is deleted by typing
an array, one's for retained and zero's for oaitted observations, followed by a slash and the
variable naae.

The value of the tiae-shared terainal for stfch instruction is apparent to one faailiar with
typical textbook probleas on flexible budgeting. Ordinarily, the aost coaplex problea will
require two least squares calculations and will not require aore than one decision by the
student. The case discussed here, in contrast, peraits the student to choose aaong sixteen
alternatives, peraits hia to visually exaaine (using the plot prograa) relationships between the
data sets alaost effortlessly and in real-tine, and allows hia to use or disregard data at will.
Thus he focuses on the concepts rather than being distracted by the conputatlons. This is only
possible because of the availability of the tiae-shared terainal and easy-to-use prograns.

The capstone section of the course is a study of corporate financial planning nodels, their
characteristics, users, and liaitations. Such nodels have only recently been developed, but are
rapidly spreading in use aaong the larger and aore progressive corporations. At present the
student's only exposure to financial planning nodels is through periodical readings since they
have not yet appeared in textbooks. No approxination of such a planning technique was available
prior to the development of conputerized nodels. If one looks for an earlier expression of the
concept, the hand-generated budget is the best available even though the scope of a financial
aodel far surpasses any such budget both quantitatively and qualitatively.

Following a general study ot corporate planning nodels, the student is given a duplicated
description of a coapany, its objectives, goals, operations, and environnent. The packet
contains the aost recent run of the five-year financial plan, and several proposals concerning
new investaent outlays and asset redeploy nents. The financial plan reveals that the corporate
objective of sales growth will be net if the plan is adopted and achieved, but that a planning
gap exists between planned and target earnings, and betweon planned and desired corporate
liquidity.

A corporate financial planning aodel is available via the tiae-shared terainal, which aodel
the student uses to deteraine the iapact of each proposal on tho achieveaent of corporate
objectives. Using an interactive prograa, the student changes only those Inputs necessary to
effect the changes iaplied by a proposal and receives as output the resulting five year
financial plan - balance sheets, incoae stateaents, cash requirenents,. and analytical ratios. Nor
does the student consider the aodel and the terainal a "black box," since he has previously
studied wbat the aodel does and how it does it. Thus this final coaputer exercise and related
study afford the student a knowledge of how top aanageaent planning is conducted and allows hia
to use the aost powerful planning tool available to corporate aanageaent.

The use of the corporate planning aodel siaultaneously illustrates that businessaen, rather
than aaxiaizing soae single objective such as profit, have aultiple objectives, and that a
rather vague, but real trade-off exists between these objectives. The student is not only told
through reading and lectures that the management process is heuristic in nature, but through
using such solution devices, he experiences a trial and error approach. Dewey said that "people
believe the extent that they participate." This is certainly true of students of planning and
control s y stems. Bather than the course being soiething that the student is told, it is
something that he does. And this difference between hearing and doing represents a new dimension
in the learning process.

Conclusions

The use of tine-shared renote terninalc as a student tool in the learning process at The
University of Texas at Arlington has resulted in significant inprovenents in the teaching of
corporate planning and control. The student has discovered that statistical tools acquired in
earlier courses have practical application in subsequent courses and in addressing practical
business probleas. Planning and control concepts and nodels have becoae an experienced reality
rather than soaething to which he has been "exposed." The coaplex nature of the aanageaent
process and anbiguities encountered in business probleas are recognized since the student is
required to aake tentative decisions in solving cases without having all the possible
iaplications stated beforehand. He arns that unique decisions do not exist and are not
expected.

This is possible despite tbe use of ».he coaputer which is nuaber-oriented and intolerant of
aabiguity, and because the conputer frees the scholar to study the discipline free fron the
fetters of coaputational liaitations.

Thus the realisa of the study is a function of the ingenuity ot the professor. The
challenge is appalling, but the race is stiaulating.

«6

BOX WITH SPIROGRAPHS by Gerald Salisbury
Problems Take a spirographic form, develop a new format for representation

ERLC

THE IMPACT OF COMPUTER-BASED INSTRUCTIONAL METHODS
IN GENERAL CHEMISTRY

J. J. Lagowski, S. J. Castleberry and G. H. Culp
The University of Texas
Austin, Texas 78712
Telephone: (512) 471-328B

Introduction

In the past the use of computers in the educational process has been generally limited by
systems and software focused primarily on supporting calc u la t iona 1 or iata processing efforts.
However, recently there have been reports describing the production, use, and evaluation of
programs designed tor. use directly in the in., ructional process.

There are two major aspects to the educational process; the teacher teaching and the
student learning. All too frequently teachers become overly involved in attempting to help
students learn in a poor environment, rather than teaching; thit is, they have the burden of
assigning, grading and giving students feedback on homework and tests; helping students with
their assignments; and conducting tutorial/remedial drill group interactions. To a large extent
the computer can perform these tasks (on an individual basis) as well as or better than the
instructor, for the computer can be programmed to be the world's most patient tutor and has the
capability of interacting with the student as often and for as long as the student requires.
This, of course, does not diminish the teacher's contact with students but rather, makes it
possible for the teacher-student interaction to be richer in the activities which teachers
perform best: giving insights into difficult concepts, transmitting an understanding of abstract
ideas, inspiring students, and obtaining behavioral objectives in the affective domain.

Computers can be used to individualize student experiences in several ways. Programs can be
used to measure entering skills and prescribe a series of programs ^which contain remedial
materials if necessary, standard curriculum materials, and/or adva need ^placemen t materials. In
addition, each program can branch students ahead, provide extra work or help, or branch back on
the basis of the student's aptitude. Well designed programs can allow for individual differences
in learning speeds by allowing students to take a module as many times as necessary and work for
as long as desired or necessary. When the student's interest dictates, modules which supply
specialized or enriched materials can be supplied.

Instructional programs can generally be classified as tutorial-drill, laboratory
simulation, or evaluation. With computer-based interactive programs it is possible to provide
the student with tutorial-drill materials (practice problem sets, question and answer sessions,
problem situations, etc.) which are tailored to his needs and are unique to him. Programs which
simulate laboratory experiments can be used to extend a student's laboratory experiences to much
greater depth than ever before possible; that is, the student can perform a greater variety of
experiments more often if necessary, and each time collect unique data. The time
compression/expansion capability of the computer allows the student to perform experiments which
in the real world occur on a very short time base or a very long time base (e.g. kinetic
studies). In addition, computer simulations allow students to perform experiments which are too
dangerous- for beginning students to perform on a large scale in the real laboratory and to
perform experiments which are too sophisticated and require too expensive an apparatus tor wide-
scale use by oeginning students.

Consider a general chemistry course composed of a lecture segment, a laboratory segment, a
reading segment, a homework segment and a testing segment, in lecture, CAI methods can be used
to take some of the burden of helping students learn from the instructor [ i.e. working examples,
problems, illustrating mathematical models, etc., where facilities exist for mass display
(overhead projection or closed circuit T.V.)]. In laboratory, computer methods can supply
tutorial/drill materials and simulations. In the homework segment, drill and practice and
remedial work can be supplied by the computer. In the testing segment, the computer can generate
exams, administer and grade minimum level exams and make-up quizzes. In all of the segments, the
computer can be used to keep records and calculate grades. Figure 1 summarizes these
app 1 ica t ion s.

If these applications strike you as worthwhile, you may still be wondering if they are
economically feasiole. This is a question highly dependent upon local conditions and facilities.
Where time-sharing computer facilities already exist, these applications are quite feasible and
require very little actual com pu ter time. Where there are no prior existing facilities, mini-
computers may still provide an economical means of implementing computer methods. Some possible
hardware configurations and estimated costs are shown in Figure 2.

’77

Course

Lecture

Laboratory

Readings

Homework

Testing

Supplementation

Examples ,
Tutorial/Drill ,
Record keeping,
Grading

Tutorial/Drill ,
Simulations ,
Record keeping,
Grading

Generate ,
Bibliographies

Drill G Practice,
Remedial Work
Record Keeping
Grading

Minimum level
make -up ,

Test generation,
Record keeping,
Grading

FIGURE 1.

Previous investigations conducted under carefully controlled experimental conditions using
general and organic chemistry students have consistently indicated tnat computer-based
instructional techniques exert a positive effect upon student performance in the attainment of
course ob jectives[ 1 -4 ].

In addition, students have consistently and overwhelmingly indicated positive attitudes and
opinions in favor of computer techniques applied to instruction. When computer techniques are
presented to students as supplemental material they tend to view them as aids rather than as
another dehumanizing barrier between the student and instructor. As a supplement, the computer
can remove the burden of stereotyped activities from the teacher and allow him more time tor the
activities which he performs best.

There are many different ways in which computer methods can be applied to the educational
system and many different philosophies motivating and guiding their use. We take the position
that computer methods should:

1. Supplement, not replace the existing course.

2m 3e designed to help students learn, not necessarily to teach or merely transfer
standard information.

3. Help to individualize student experiences.

4. Provide the basis for a self-paced instructional approach tor the student.

With these ideas in mind, an experimental Chemistry 302 course was offered in the Pall of
1971, with the following characteristics:

£ou£§e fie§C£i£tion

The existance, or creation of instructional material for use with computers automatically
leads to a modularization of the subject. Accordingly the experimental 302 course appeared from
the student's view in modular form. The conventional three con tact- ho urs per week were designed
as one hour per week in formal lecture, small group discussion, and at a computer terminal. The
first two interactions were at the time scheduled for the course; one hour of terminal time was
assigned at the convenience of the student. Students could have more computer time on a first
come - first serve, sign-up basis.

The course content was that agreed upon with the coordinator, viz.. Chapters 7, 9, 10, 11,
13, 14, and 15 in Slabaugh and Parsons.

i££tures. One hour per week was used in formal lecture to present broad concepts and
attempt to draw apparently diverse material together, but with a minimum of examples neinq
worked in class. A ten-minute quiz was given at the start of each lecture over the material of
the previous week. Occasional demonstrations were performed.

discussion Periods. This hour was devoted to student discussion and problems. The students
dictated the course of the discussion, and, if desired, problems were worked out in detail. No
attempt was made to lecture during this hour.

SiJilSai Te£mina^ Time. The assigned hour at a terminal[5] was used ay students working with

programs classified as 7*7 tutorial, (b) simulated experiments, or (c) examination. A list of

the programs in categories (a) and (b) appears in Table 1. The programs in category (c) were

essentially drill and practice problems sirtlar to those gi'en on the 10 minute quizzes and

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'Total coat including maintenance amortized over a 5 year period and baaed upon 80 % uaage factor
An applied to a ayatem in which the 16 terminate are hardwired

TUTORIAL MODULES

iapter

Code

Description

Points

CHEM1

The Gas Laws

CHEM114

Henry’s and Raoult’s Law

CHEM116

Colligative Properties

CHEM113

Solution Concentration

CHEM2

Solution Stoichiometry

CHEM119

Equilibrium

CHEM107

pH, [HO, pOH [OH-]

CHEM124

Common Ion Effect

CHEM126

Ksp

CHEM36

Redox Equations

CHEM109

Elementary Thermochemistry

CHEM139

Thermochemistry

SIMULATED EXPERIMENTS

CHEM3

Molar Volume of Nj

CHEM115

Colligative Properties

CHEM32

Reaction Kinetics

CHEM122

pH and Determination

CHEM19

Titration

CHEM127

Faraday ' s Law

CHEM41

Calorimetry

TABLE 1

aajor examinations. Copies? o f typical student interactions tor these urograms are available tor
inspection.

In this ey per inent, there was no limit pla ed upon the number ot times a student might
interact with any of the programs described. That i: he could work at the mater: al until he
reached the level of achievement he desired.

This course, in addition to presenting the student with self-paced nodules, was organized
abou*. the yeneral principles of continyency ma nagemen t[ 6 ]. Brietly, a relftionship is
established between a response and a subsequent event. Responses correspond to student behavior
and th subsequent events are the reintorcers tor this behavior. Classical l v these arc the
grades given at the end ot a semester after the student has performed to some level ot
accomplishment. As has been stated: "Final grades, Like most sociaL rewar Is, however, are large
events that are awarded atter a long delay and not in any specitie' relation to easily
identifiable responses. Xn order to be useful with a continyency management system, the tinal
grade must be divided into smaller parts which can be made availaolu to students throughout the
semester. "[ 6 ] one obvious way of accomplishing this end in a mod ul \ r iz ized course is in term; ot
the total accumulated points from each module completed to a given level ot achievement.
Accordingly, eacn module was assigned a point value which reflected its relative contribution to
the total coUise material (Table 1). In addition points were assiyned tor (a) attendance (which
was not require^) at lecture and discussion/ (b) quizzes, (c)aajor examinations. The point
schedule is given in Table ?. Grades were assigned on the following basis: a = 10U-9UX, B ~ 39-
0OX, C - 79-70* , 0 = 69- 80%, F = below 60%.

Three major examinations (two hours each) were given at night. Each ot these examinti)ns
covered about 1/3 ot the material in the course. There was no comprehensive tinal examination.

Results

Two traditional 302 courses were used tor comparison with the compute* supplemented 302
course. Figure 3 and 4 show the Standard Achievement Hath Test and Standard Achievement Verbal
Test score distribution tor the three sections. From these we see that the three sections have
approximately the same range and distribution of scores.

In Figures 5 through 7, score distributions of the quizzes and tests are shown, a
distribution for the paper-pencil tests and a distribution ifter students have had ai
opportunity at computer make-up. Figure 8 summarizes the means on the t3sts and quizzes.

Figure 9 gives an indication of the degree of use ot the computer make-up as well as the
kinds of students using the make-up. Figure 10 indicates the usage of the computer tutorial and
simulation modules.

Figure 11 shows the grade distribution in the corapu t er-suople men t ed section and the two
comparison sections. In Figure 12, a comparison of the drop ratas between the supplemented
section and one traditional course is shown.

In Figures 13 and 14, cost factors are tabulated. Figure 13 shows authoring and debugging
costs while Figure 14 shows student usage costs.

Riscjjssion

In this experiment it is evident that the use of supplemental com pu ter-Dased instructional
techniques exert a positive influence upon student performance. While the SAT scores tor the
experimental group result is essentially a normal distribution, as seen in Figures 3 and 4, it
is interesting to note in Figures 5 and 6 that the distribution of scores for TEST 1 and TEST 2
2£io£ to the computer jnake -up indicate a general shift toward a higher achievement level. TEST 1
and TEST 2, in comparison with TEST 3, covered areas that had a higher degree of computer-
supplemented materials available tor student use. The results of the latter examination (Figure
7) appear to reflect this. Thus a comprehensive comparison of the three exams tei ' s o indicate
a degree of correlation between achievement and access to coapu ter-supplerae nte i instructional
t echn iques.

The influence ot self-paced individualized computer-based examination make-up is
dramatically seen in Figures 5 through 8. In every instance of student performance evaluation,
the existence of computer-based instructional techniques allowed a much greater number ot
students to attain a high degree of proficiency in specified behavioral objectives. The
majority of students making use of the computer examination make-up appear to be either the
lower or slower achievers within the class (see Figure 9), further illustrating the marked
effect of computer-based self-paced individualized instruction on the instructional process. The
carry-over of these results is clearly evident in Figure 11. Seventy percent of the experimental
class gained at l'jdst a 90X proficiency in the course objectives, while the traditional classes
indicate a more normal distribution of semester grades.

GRADING SCHEDULE

ITEM

MAXIMUM POINTS

MAJOR EXAMINATIONS

(100 each)

300

QUIZZES

(10 each)

100

DISCUSSION PERIODS

(3 each)

LECTURES

(3 e< ch)

SIMULATED EXPERIMENTS

160

TUTORIAL MODULES

135

TOTAL 776

100 - 90% = A

89 - 80% = B

79 - 70% = C

69 - 60% = D

Below 60% = F

TADLE 2

FIGURE '3

FIGURE 4

FIGURE 5

n fi I J SCORE’S

FIGURE 6

FIGURE 7

TEST AND QUTE MEANS

T1 T? Tj Q1 Q2 Q3 Q4 Q5 06 Q7 Q8 Q9

TEST MEAN

60.4 62.9 43.3 3.7 5.4 5.3 5.8 6.7 5.7 4.4 5.5 6.5

TEST MEAN AFTER COMPUTER MAKF-UP

85.1 90.1 81.1 9.0 8.4 8.4 9.3 12.8 9.8 8.7 8.4 8.9

FIGURE 8

COMPUTER TEST USAGE

STUDENTS

TAKING TEST

113

115

111

109

105

102

100

115

110

101

STUDENTS

TAKING COMPREHENSIVE

MAKE

-UP

STUDENTS

SCORING BELOW 70%

103

STUDENTS

BELOW

70%

TAKING COMPREH':

NSIVE

MAKE-

-UP

FIGURE 9

C 3
<
00
D

&«

r-rHjrcnu5fHLOcDr'

cocdooco^ocdcdoo

CO P- rH
CO 00

r 1

FIGURE 10

COURSE GRADE DISTRIBUTIONS

A B

CDF

COMPUTER

SUPPLEMENTED* 70% 9.7% 6.1% 1.2% 13%

TRADITIONAL

CLASS* 10.4% 25.6% 18.4% 14.4% 31.2%

TRADITIONAL

CLASS 18.7% 33% 26.4% 12.7% 9.2%

* SAME INSTRUCTOR

FIGURE 11

CHEM122

DROP RATE

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 It 16 17 18

WEEK

TRADITIONAL SECTION 16%

COMPUTER SUPPLEMENTED SECTION 19%

FIGURE 12

AUTHORING 6 DEBUGGING COSTS

# MODULES

iM. HRS.

COMPUTER COSTS

SUPPLIES

PERSONNEL15 COSTS

86a

11.097

$2885.36

$596.87

$14 ,000

a. Ec’iivalent to 44 student-terminal hours of instruction.

b. Twelve man-months of authoring and content debugging; 9.S man-months
of cocing, debugging, and general manage- ;ent.

FIGURE 13

STUDENT USE COSTS

0JOBS

TM HRS*

COMPUTER COSTS

LINE COSTS

STUDENT HRS

2291

18.944

$4925.48

1613.57

RATIO

COST/ STUDENT HR STUDENT HR/TM HR
4.05 85/1

* TM HRS = CPU HOURS +' PERIPHERAL OPERATIONS TIME FACTOR
COMPJTER COST FIGURED ON THE BASIS OF $260/TM HR

FIGURE 14

It aay be seon in Figure 12 that the drop rates of the traditional and experimental courses
are essentially the same, except for a slight increase in drop rate tor the experimental class
following TEST 1.

Figure 13 su««arizes the developmental costs for 86 computer modules. These figures
indicate a cost of approximately $200/module, including computer line time, supplies and
salaries tor personnel. It is important to note that very careful planning and design go into
the development of a module, and its lifetime should be considerable. Thus, following initial
development of a module, the only additional cost comes from up-dating or revision and would be
ncg 1 igible.

In Figure 14, the cost of 2,291 student interactions is summarized. The figures indicate a
cost of approximately I4.0U per hour of student connect time, or about $2.85 for each student
interaction, based upon a line charge of $1.00 per connect hour and rate of $260.00 per computed
Tfl hour.

Summary.

The development of computer-based instructional techniques to augment a traditional course
led to modularize ion of the course. This, in turn, resulted in a clear and comprehensive
description of tne course in terms of specific behavioral objectives. The combination of
modularization and computer-based instructional techniques provides a unique approach to self-
paced, individualized instruction.

The results of the study described in. this paper indicate that this combination of course
design and instructional techniques yields a very positive effect upon student performance. This
effect is particularly evident in the use of computer-based examination make-up for the
attainment of specified behavioral objectives. Seventy percent of the class attained a 90* or
better proficiency in the course objectives.

The cost of development averaged approximately $200.00 per module and the cost of student
utilization averaged abour $4.00 per connect hour. A total of 86 modules have been developed tor
use in undergraduate chemistry instruction.

ACKNOWLEDGEMENT

This study was conducted under grants from the floody Foundation and the Esso Education
Foundation. Special acknowledgement and gratitude is hereby extended for their generosity and
belief in educational evolution.

REFERENCES

1. s. J. Castleberry and J. J. Lagowski, "Individualized Instruction Using Computer

Techniques," J.. Chero. Ed^ 47 91 (1970).

2. S. J. Castleberry, E. J. Montague, and J. J. Lagowski, "Computer-Based Teaching Techniques
in General Chemistry," Res.. Science Teach. 7 197 (1970).

3. L. H. Rodewald, 3. H. Culp, and J. J. Lagowski, "The Use of Computers in Organic Chemistry
Instruction," J. Chenu Ed^ 47, 134 (1970).

4. G. Li. Culp and S. J. Castleberry, "Computer-Assisted Instruction in Undergraduate Organic

Chemistry: An Evaluation of Selected Programs," Science Education, 423 (1971).

5. Two types of terminal devices were used, teletypes and a teletype-slide projector
combination. In the latter case it was possible to include visual displays (e.g., colors of
indicators at different pH's) in the programs. The slide projector was computer-controlled.

6. K. E. Lloyd, "Contingency Management in University Courses,” Educational Technolo^, April,
1971.

C ON PUTEfi- AIDED ClASSBOON CHKNISTR Y INSTRUCTION VIA
INSTANTANEOUS VIDEO PROJECTION OP TELETYPE OUTPUT

Bonald H. Collins
Eastern Nichigan University
Ypsilantl, Nichigan 48197
Telephone: (313) 487-0 106; 487-0423

The use of computers for instructional purposes in the chesistry curriculus norsally
involves a 1:1 student-conputer interaction- This cottunica tion can be either via batch
processing or renote teletype in tine-shared node. Furthermore, the role of the nachine can
range from that of surrogate teacher to sisply a high-speed calculator perforning data
reductions however, all forns of educational conputer utilization can be broadly classified as
cor ''u ter-aided instruction (CAIDI). This general classification can be further subdivided into
co. ju ter-assisted instruction (CAI) , conputer-evaluated instruction (CEVIN), and aon-interacti ve
computer application (NICA). The criteria used for determining these categories as well as their
relationships one to another are presented in Table I. further information on this
classification scheme for computer usage is given in a previous review by this author[1]. In
particular, this earlier review covers methods for teaching programming languages and optimizing
the role of NICA in the chemistry curriculum; consequently, these topics will not be discussed
in the present paper. Instead, the emph, is will be on techniques and pedagogical strategies for
Hqroupn CAIDI; i.e., the effective use ofc on-line computing in the classroom as a component of
the normal lecture environment. This usage is neither clearly CAI nor NICA, but rather
incorporates some of the features of each. The extent to which on-line classroom computing
becojes at least "pseudo CAI" depends on t\e extent to which the program used includes
interrogational features and remedial branching, without these characteristics the principle
goal is the expansion or clarification of course content and hence the category is more properly
NICA. In either case the nachine is now simultaneously interacting with an entire class and
hence the designation "group CAIDI."

To date, on-line computing during a lecture class has not been extensively used, primarily
because of technological problems associated with presenting the results in a visual form
suitable for large audiences. However, the recent development of a low-cost adapter [2] for
instantaneous video projection of teletype output has made on-line computing a more practical
classroom technique. By having a room equipped with only a telephone line and suitably-sized
television sets an instructor can now routinely supplement his lectures with the results of on-
line computing provided a portable teletype terminal is brought into the classroom. Actually,
this configuration for on-line lecture ball computing is only one of several possible
arrangements. A summary of the various possible configurations is given A Table II. It would
seem, however# that this method employing the video adapter is definitely superior to, as well
as being much more convenient than, the use of either a television camera or overhead projector
as the transmitting link into the viewing medium. Utilizing *i TV camera effectively requires
that the instructor have a technical assistant present during his lecture and essentially
converts the classroom into a television studio wbich distracts somewhat from the desired
educational environment. Having the teletype output printed directly on plastic transparency
material t’hich is then projected onto an opaque screen via the use of a standard overhead
projector is technically feasible and coamercially available in the form of a teleprinter
pro jcctor [3] , but the clarity of the output lor mass viewing does not compare favorably with the
video technique.

The video adapter currently under discussion is compact, measuring 3 x 6 x 12 inches, and
is equipped with the appropriate cables for easy input connection to a model 33 teletype and
output connection into a video receiver. This commercially available device is low-cost and
comes equipped with a switch which permits the user to disable the teletype and merely get the
video output without accompanying bard copy. The principal advantage of this capability is that
the teletype is silent and the lecturer need not speak over the background of mechanical noise.
The disadvantage, of course, is that there is no permanent record of the results. The adapter
cones in several models, but the one currently being used for chemistry instruction at Eastern
Nichigan University is capable of displaying an image consisting of 8 vertical lines of output,
each 32 characters in length. This has provided excellent viewing in a classroom with
approximately 100 seats and 4 ce iling- mounted 25-inch television sets.

Turning now from the technical aspects of on-line classroom computing to the pedagogical
aspects, it night be well to begin by suanarizing the advantages of this instructional
technique:

1. Provides for rapid, accurate calculations and
neat, orderly display of the results.

2. Pernits the use of sophisticated, accurate

100

TABLE I

CLASSIFICATIONS FOR INSTRUCTIONAL COMPUTER USAGE

COMPUTER-AIDED INSTRUCTION
(CAIDI)

Is there a continuing, on-line student-computer dialog in which the machine is
interrogating the student or directing the logical development of a new concept?
Is the communication pedagogically interactive or tutorial in nature?

YES

Computer-Assisted

Instruction

(CAI)

la the
in the
course

principal role of the computer
development and grading of
assignments and examinations?

YES

The principal role of the computer must then
be to process course materials, expand course
content » or to merely provide student experience
with the various ways in which the computer is
utilized in chemistry.

Computer-Evaluated

Instruction

(CEVIN)

Non-In ter active Computer Applications (NICA)

ERIC

mathematical methods rather than the
approximations often used for convenience.

3- Introduces the students to computer program

which can subsequently be used for outside assignments.

4. Provides a focus for active classroom discussion;

i.e.f via a nultinedia three way instructor-student-computer
interaction.

5. Brings a dynamic, nodern "instrument"
into the ciassroon.

Based on our experience to date at Eastern Michigan University the ciassroon computing
technique is very effective provided that:

IS not used tqq fifianegtiy; i.e. , if on-line computing is used during every lecture in a
given course, then just as with any other instructional aid, students will become somewhat
bored with its use.

2. It® applications are carefully selected so as to truly reinforce or expand upon some topic
under discussion, it is imperative that the data reduction or simulations performed be
those which truly require mathematical accuracy not otherwise obtainable by approximation
methods, or require the rjapid use of mathematical operations (e.g.v iteration techniques)
not otherwise possible in real time during a lecture. In other “ords, the computing medium
is not the complete message in itself, and the technique must not be exploited purely for
its theatrical value during a lecture.

TABLE II

POSSIBLE CONFIGURATIONS FOR ON-LINE CLASSROOM COMPUTING

3. A EiPld nipom tiling ht dog network employed which provides access to a reasonably
large library of appropriate stored coaputer programs.

4. Ifcf rtudfots AlU laiil 12 lAl 111S HSflllM for use outside of the classroom. This can be

accoaplished either by using the identical progras in time-shared aode or by providing an

analogous batch version of the progran. In either event it is very inportant that any
interested student be able to experinent on his own with the sane type of calculation
perforned during the lecture. This not only pernits repitition if necessary bat it also
allows the student to pursue other examples of his own choosing.

The potential applications of this technigae for the classrooa use of on-lise conputing in

chenistry education are probably unlinited and certainly too nunerou; to list; however, a few

exanples are given in Table III. For nore exacting delineation of the types of prograns
involved, t examples which have been used quite successfully in our general chenistry coursn
are shown n Figures 1 and 2. Each figure contains both a listing of the program and a sample
output. The first example is on the topic of ionic equilibrium and the progran has been written
to provide a comparison of the pH values calculated tor an aqueous solution of a weak acid,
depending on whether a simplifying mathematical assumption is employed or the complete quadratic
equation is solved exactly. This permits a rapid, accurate demonstration of the influence which
the magnitudes of both the ionization constant and the concentration of the acid have on the
validity of the assumptions often used to avoid solving a quadratic equation in this type of
equilibrium problem.

1..JLE III

SAMPLE UTILIZATIONS OF ON-LINE CLASSROOM COMPUTING
IN THE CHEMISTRY CURRICULUM

Mathematical Operation (s)
and/or

Topic

Computing Mode

£auss?J5i.

Ionic equilibrium
calculation

Data reduction via exact solution
of quadratic equation

general chemistry
quantitative analysis

Real gases

Data reduction via iteration solution
of higher order polynomials

general chemistry
physical chemistry

Thermodynamics

Rapid data reduction using stored
database

general chemistry
physical chemistry

Titration

phenomena

Curve fitting, analysis of data via
derivative appt oximations, graphical
simulation

general chemistry
analytical chemistry

Identification
of unknowns

Data evaluation via comparison to
stored database

organic qualitative
analysis
x-ray powder
dif fracti on

Inf orna tion

retrieval

Keyword searching of stored
database

chemical literature

The second sample program is concerned with the topic of real gases as depicted by the van
der Uaalfs equation in comparison to the mor e-frequently used ideal gas model. Again, the
program is constructed so as to permit a rapid, yet accurate comparison of the answers obtained
from the two possible equations; i.e., the real gas equation and the PV=nRT ideal gas version.
The mathematical approach used in the program is to first solve the ideal gas equation for the
apparent volume occupied by a given quantity of gas under specified conditions of pressure and
temperature, and then to use this ideal value as the first approximation for an iterative
solution of the more exacting van der tfaalvs equation. In this way it is easy to dramatize to
the students those physical conditions which either maximize or minimize real gas deviations
from ideality. Furthermore, when used in a freshman level general chenistry course, this progran
introduces the students to the powerful numerical method of iteration. Although the students nay
not fully understand the mathematics they will certainly appreciate the obvious value of the
iteration technique for chenistry applications.

FICURE 1

IONIC EQUILIBRIUM PROGRAM

10' THIS PROGRAM WAS DEVELOPED FOR ON-LINE CLASSROOM COMPUTING
15' BY SUDHIR VAIDYA UPON DR. COLLINS' REQUEST.

85 REAL QH30.QPCT.QPH

89 PRINT '* FOR HOW MANY ACID CONCENTRATIONS WILL PH BE CALCULATED?"
30 INPUT.N

40 AK-I .0E-5

49 PRINT ” WHAT IS YOUR INITIAL ACETIC ACID CONCENTRATION IN M/L?"

50 INPUT.HAC

55 PRINT ” WHAT IS YOUR CONCENTRATION INCREMENT?"

56 INPUT. X

60 B-AK*AK

61 PRINT

68 PRINT 105.

63 105 FORMAT C9X»" PH"6X. "EXACT PH"/)

70 DO 101 I — I . N
80 TEMPI -AK*HAC

90 H30»SQRT( TEMPI )

100 PCT10N»100.0*(H30/HAC)

ISO PH*CL0G(H30))/8.3026*-l .0
130 TEMP2»B*t4.0*HAC*AK>

140 QH30*< -AK*SQRT( TEMP2 ) )/2 .0

150 QPCT-(0H30/HAC)* 100.0

160 QPH“L0G(QH30>/2 .3026**1 .0

170 PRINT 102. I.PH.QPH

180 102 FORMAT ( IX. I3.4X.F7.4.4X.F7.4)

190 HAC»HAC-X'

200 101 CONTINUE
210 END

PHHAC 12149 01/21/72 FRI .

FOR HOW MANY ACID CONCENTRATIONS WILL PH BE CALCULATED?

7 5

WHAT IS YOUR INITIAL ACETIC ACID CONCENTRATION IN M/L?

7 0*001

WHAT IS YOUR CONCENTRATION INCREMENT?

7 0*0001

EXACT PH

1 3*8723

2 3.8952

3 3.9208

4 3.9498

5 3.9833

3*9015

3*9259

3.9533

3*9846

4.0208

FIGURE 2

CAS LAM rROGUm

5' VAN DER VAALS EQUATION

10* THIS PROGRAM VAS DEVELOPED BY SUDHIR VAIDYA UPON
15* DR. COLLINS' REQUEST IN JULY 1971*

16 DIMENSION GAS( 1 >

80 PRINT

30 PRINT ” SOLUTION OF VAN DER VAALS EQUATION BY ITERATION"

31 PRINT
38 PRINT

80 PRINT " TYPE THE NAME OF THE GAS."

88 INPUT 8002 . GAS
83 2002 FORMAT CA6)

85 PRINT 200 l . GAS

87 2001 FORMAT! IX. "VAN DER VAALS CONSTANTS A AND E F0R"2X. A6."ARE")

89 INPUT. A.B

90 PRINT " TYPE THE VALUES OF - T.P. N» CONV ERGENCE FACTOR AND THE

91 ♦ MAXIMUM NUMBER OF ITERATIONS*"

100 INPUT.T.P.SN.C.MNI

110 N“1

115 R-0. 082056
120 V-SN*R*T/P
130 PRINT 1001. V

140 1001 FORMAT t/1 X." USING IDEAL GAS EQUAT1 0N"/10X."V- “F 10.6//)

150 1608 VV«< SN*R*T )/(P*A*SN*SN/(V*V)>*SN*B

160 PRINT 1002. N.VW

170 1002 FORMAT 1 1 4. SX. F10 .6)

180 D-ABStVV-V)

190 V-VV
200 N-N«-l

210 IF (D-CJ999. 999. 1003

220 1003 IF (N-MNI) 1808.1808.1010

230 1010 PRINT " NO CONVERGENCE."

240 999 END

SOLUTION OF VAN DER VAALS EQUATION BY ITERATION

TYPE THE NAME OF THE GAS*

7 002

VAN DER VAALS CONSTANTS A AND l FOR C02 ARE
1 3.59.0.0427

TYPE THE VALUES OF - T.P. N. CONVERGENCE FACTOR AND THE MAXIMUM NUMBER 0
r ITERATIONS.

1 50.10.10.0.000001.100

USING IDEAL GAS EQUATION

V» 4.102800

8
9

I .736661
•744967
.489459
•454198
•450442
.4500 58
.450019
.450015
.450014

105 ,94

IB BBBBarr# ClBSStOOS COBPBting 1b B VBiMBblB BIMfc to t«achiB9 BBd B SOdBCB

technological development which should not b« overlooked, particularly in any institution where
tine-shared coiqputing is available and where television facilities are either permanent
classroom fixtures or are available in portable models. In such an environment the only required
installation is a telephone line into the lecture room. The cost of the described adapter is
relatively modest and the physical problems associated with moving and handling the con^onents
of the apparatus! i.e., teletype, adapter, and the video sets (if not permanently mounted) are
not insunsountable. In fact, with a little practice, the equipment problems are no greater than
those usually encountered with the use cf movie projectors, and the dynamic, real-time,
unrehearsed nature of the computing approach is pedagogically much more rewarding. The role of
the television display of the computed output as a focus for classroom discussion also cannot be
overemphasised. Asking for student responses regarding appropriate input parameters and/or
output values often promotes extremely active, and sometimes controversial, discussions in the
classroom. Finally, this method displays the power of computing as a modem, relevant scientific
and instructional tool to mass audiences, some of whom may not otherwise be exposed at all to
computers and computing technolgoy.

REFERENCES

1. R. W. Collins, "Teaching Programming Languages and Optimising Nor-Interactive Computer
Applications (NICA) in the Chemistry Curriculum," Proceedings of the Second Annual Conference
on Computers in the Undergraduate Curricula, 99-110

2. Manufactured by Ann Arbor Terminals, Inc., 6107 Jackson Road, Ann Arbor, Michigan.

3. Manufactured by I. P. Sharp Associates Limited, Computer Products Division, 320 Queen Street,
Suite 2206, Ottawa 4, Ontario CANADA.

PITT'S INTERACTIVE GRAPHICS AND
CON PUTER- GENERATED REPEATABLE EZAfllNATION SYSTEMS

H. F. Sliwinski. and K. J. Johnson
I'niversitf of Pittsburgh
Pittsburgh, Pennsylvania 15213

Several applications of computers in chomical education have been triad at Pitt during the
past 3 1/2 years. These includa CAI, use of canned programs for data reduction ant? simulation,
use of an interactive graphics system, and teaching computer programming as part of the
undergraduate curriculum! 1 ]• Ttiare is evidence that the impact of these efforts on the quality
of our undergraduate instruction is favorable, so these projects are being continued and
axtended. This paper describes two new projects: A teletype-oriented interactive graphics system
and a question-format based coi pu ter- generated repeatable examination system.

Intgcicii ye ££afilli£§

One of the earliest interactive graphics systems is the Culler-Fried System at the
University of California at Santa Barbara[2]« The NSP recently supported a network consisting of
ten universities around the country connected yia phone lines to the UCSB Computer Center. The
graphics terminal configuration is shown below.

Keyboard

The grant provided the hardware, communication costs, computer tine, etc. for one year. Re are
now developing the software and hardware required to provide essentially the sane graphics
package on Pitt's PDP-10 time-sharing system. The software problem was tackled first.

Wo have written an interactive graphics package, modelled after the Culler-Fried system, in
FORTRAN. The program reads a 72 character line of instructions from a teletype terminal, decodes
the line, executes the instructions, and requests the next line. The following example
illustrates the power of the system for simulation applications.

Two-site NHB exchange, givan several simplifying condx Hons, gives the following line shape
f unct ion r I (vj :

= rr r yT .22, ?2~ tt~

[ i (vA+vb) " + t (va-v) (vb-v)

where K is a normalizing constant (taken as unity) , t is the lifetime, va and
VB are resonance frequencies of sites A and B, and v is the frequency! 3 ]. It 2ttt^va“vb^ > ^ 9

two lines result. The two peaks coalesce when 2ttt^va“vb^ = ^ 9 an<* sharpen as this value

decreases. In this example O^y^lOO, vA = 33.3, vB = 66.7. and t is an imput variable. The

following routine is a *jser program stored on the disk.

108

LVL2 CTX 71 ID + .1 * 50 STORE V SUB 1

LVL1 LOAD 33.3 STOnE A LOAD 66.7 STORE B LOAD 3*14159 STORE P
LVI£ LOAD V - B1 Sft STORE I

LOAD V - A1 SQ * I * 4.0 * PI * PI * T1 * T1 STORE I
LOAD V - 50.0 Sft + I INV * T1 * 33.4 * 33.4 STORE I DISP -

the proqran has the naae BICH. A saapls .i.cutioo follows:

.RUN PIGS

ENTER INPUT LINE (7*A1)

LVU LOAD 0.01 STORE T MY EXCH

Y MAX = 5.1589E-02 X MAX = 1.0000E+02

** **

* *

**#■***+*#■*

- X MIN = O.OOOOE-Ol

END OF USER PROGRAM EXCH

Y MEN » 5.0763E-O4

ENTER NEXT LINE.

CPU TIME: 1.85 SECONDS

The program EXCH vas craated and edited using a text editor. LVL1 and 171.2 specify scalar
or vector node. CTX denotes the dimension or length of vectors on LVL2. The arbitrary upper
linifc on the length is 71 coipoaents per vector. ID generates the vector -1 * value ( ♦ 1, and
assigns these values to two woe king registers corresponding to the X and T axes. SUB 1 assigns
the values in the register corresponding to the T axis to the X axis register. LVLl variables
■ay be used in LVL2 expressions by adding a 1 after the variable naae, for exaaple, Pi. SO
stands for square and IHV for invert.

The Culler-Pried pseudo-aaseably language is sathesatically oriented and quickly learned by
students with soae previous progtasaing experience. He have used it to simulate the follovitg
chenical systeas: siaulation of HHB spectra, plotting of radial distribution functions, kinetic;
scheaes, acid-base titrations, solubility effects, potentioaetr ic and coaplexoaetric titrations,
and others.

The graphics systea has been used by students in a nuaerical aethods cheaistry course[4]
and by soae students vho undertake a senior research project.

aeggatjkls Siaiiaatiaas fccae)

floore and Prosser at Indiana University have deaonstrated the feasibility and advantages of
a CGBB systea[S]. They generate tests of equivalent difficulty fron a database containing test
itea3* The approach taken at Pitt is to v/rite subroutines defining the itea fornat* Por
exanple,

Hov aany grans o _ _, _ _ _ can be aade froa

grass of and _ grans of _?

The blanks are filled in by a subroutine that identifies this itea, and contains the
reguired list of compounds, ranges for randon nuabers, etc.

. m* }
* i*

HOW MANY GRANE OF ALUMINUM OXIDE, AL203, CAN BE MADE FROM
42.3 GRAMS OF AL AND 40.2 GRAFG OF 02?

13?.

B) 122.

79-9

D) 85.4

NONE OF THE ABOVE

other examples follow.

WHAT

' VOLUME OF S03 CAN BE

MADE

IF 28.9 LITERS

S02

AND 18.0 LITERS OF 02

REACT

AT ATP?

2S02 +02

■ - >

2S03

A) 3 6.0

14.4

C) 18.0

28.9

E) none of the above

A SAMPLE OF 02 WAS COLLECTED OVER WATER AT 46.6 DEGREES C. WHEN THE
BAROMETRIC PRESSURE WAS 778. MM OF HG. THE VOLUME OF THE GAS AS IT
WAS COLLECTED WAS 3.01 LITERS. WHAT WOULD THE VOLUMF OF DRY 02 BE
AT STP?

(THE VAPOR PRESSURE OF H20 AT 46.6 DEGREES IS 79.3 MM OF HG).

A) 107. B) 2.52

C) 2.37 D) 3.24

E) NONE OF THE ABOVE

AMMONIA IS PREPARED ACCORDING TO THE FOLLOWING REACTION IN THE
"AS PHASE.

N2 + 3H2 — > 2NH3

IF THE REACTION CONDITIONS ARE MAINTAINED AT STP, WHICH OF THE
FOLLOWING STATEMENTS IS INCORRECT?

A) 277 LITERS OF NH3 CAN BE PREPARED FROM 554 LITERS OF N2
GIVEN AN ADEQUATE SUPPLY OF H2.

B) 1 MOLE OF N2 WILL REACT WITH 3 MOLES OF H2 TO FORM 2 MOLES
OF NH3.

C) 277 LITERS OF NH3 CAN BE PREPARED FROM 4l6 LITERS OF H2
GIVEN AN ADEQUATE SUPPLY OF N2.

D) 28.0 GRAMS OF N2 WILL REACT WITH 6.0 GRAMS OF H2 TO FORM
44.8 LITERS OF NH3.

E) 1 MOLECULE OF N2 WILL REACT WITH 3 MOLECULES OF H2 TO FORM
2 MOLECULES OF NH3.

WHAT WEIGHT OF ETHYIENE GLYCOL (H0CH2CH20H, MW=62.1 G/MOLE)

MUST BE ADDED TO 8000 GRANE OF WATER TO PRODUCE AN ANTIFREEZE
SOLUTION THAT WOULD PROTECT A CAR RADIATOR DOWN TO -0.3 DEGREES
FARENHEIT ( = — 18.0 DEGREES CENTIGRADE)? (ETHYLENE GLYCOL IS
A NONELECTROLYTE.)

A) ((62.1) (-1.86) (8) )/( (-18.0) ) B) ((62.l)(-l8.0)(8))/( (-1.86) )

C) ((62.1)(-1.86))/((8)(-l8.0) ) D) ((62.1)( -0.3) )/( (8) (-1.86) )

E) NONE OF THE ABOVE

WHAT WEIGHT OF PB METAL WILL BE DEPOSITED AT AN INERT EIECTRODE ON

PASSAGE OF A CURRENT OF 61.5 AMPS THROUGH A SOLUTION OF

LEAD (IV) CHLORIIE FOR 17.6 HOURS ? THE REDUCTION REACTION IS

pb(4+) + 4e- -

- > PB

( 207. * 61.5

* 17.6

* 3600

)/( 96500

GRAMS

( 207. * 61.5

* 17.6

* 3600

) A 96500

)

G1AM3

( 61.5

* 17.6

* 3600

)/(9^5W

207.)

GRAMS

( 207.

NONE OF THE ABOVE

* 61.5

* 17.6

JA96500

GRAMS

SELECT THE PROPER SET OF NAMES FOR THE FOLLOWING FOUR
COMPOUNDS:

TI(CR01+)2 2. U(S03)3

110

997 .

3. NI(C03)

4. AU(N)

0 0*0— Pi o <

TITANIUM(IV) CHROMATE

URANTIUM(Vl) SULFITE

NICKEL(II) CARBONATE

GOLD(III) NITRIDE

TITANIUM(IV) DICl'ROMATE

URANIUM(Vl) SULFITE

NTCKEL(II) CAREOFATE

GOLD(III) NITRIDE

TITANIUM(II) CHROMATE

URANIUM(VI) SULFATE

NICKEL(II) CARBONATE

SILVER(III) NITRIDE

TITANIUM(IV) CHROMATE

URANIUM(VI) SULFITE

NICKEL (II) CARBONATE

SILVER(III) NITRIDE

E) NONE OF THE ABOVE.

The FORTRAN program consists of a BLOCK DATA subprogram, the main program and onm
subroutine for each item. The BLOCK DATA subprogram initializes several arrays that are in
COflflDH. These include element names, symbols, atomic weight, cation and anion names, etc* The
main programs contain random njaber initialization instruction, reads a Key for generation of
the test, and calls the desired subroutines.

The primary objective of this project is to allow students in the first term of general
chemistry to take the first hour exam on a repeatable basis. The computer can generate hundreds
of examinations of equivalent difficulty. These can be administered by proctors in an
examination room that is available several hours a day. The proctor can perform an item analysis
as he grades each test using tie computer-generated answer key. The item bank can thus be proved
and revised as desired.

The system has a number of other applications, students nay use it in a tutorial node to
drill selected topics. Items may be generated for recitation quizzes, parts of hour exams and
final exams. The system can generate tests for screening and diagnostics purposes. It can be
used to generate a make-up exai of arbitrary difficulty. It can be used to help students
identify this weakness in assuied background material, etc.

Conclusion

The computer-oriented curriculum development project at Pitt now has three areas of
emphasis: tutorials, simulations and testing. The graphics package described here provides a
ery powerful language with graphics output for simulation and data reduction applications. The
GSE system is adding a new dimension to our CAI tutorial-drill package and will allow us to
estructure the general chemistry curriculum.

ACKHORLEDGEBENTS

Support from the Rational Science Foundation Grants GJ-696 (graphics network) and GO-3184
institutional science development) is gratefully acknowledged. The latter grant provided
ostdoctoral support for RFS. Prof. L. E. Epstein has contributed a number of questions to the
GBE system, s. Levitt and D. dawkins have coded several items in the CGRE database. The
operation of the Computer Ceiter staff is also gratefully acknowledged.

REFERENCES

E. E. Tratras and K. J. Johnson, "Conpu ter-Assisted Instruction in Chemistry at Pitt,"
Proceedings of the Conference on Computers in Chemical Education and Research, DeKalb,
Illinois, July, 1971, p. 4-47.

K. J. Johnson, "Curriculum Development Through Computer-Based Saterials Graphics, Tutorials
and Programming Languages," ibid*, p* 5-6.

K. J. Johnson, "Computers and Chemical Education at Pitt," Proceedings of the Conference on
Computers in the Undergraduate Curricula, Dartmouth College, June, 1971, p. 130.

2- C- S. Ewig, J. T. Gerig and D. 3. Harris, "An Interactive On-Line Computing Systam as an
Instructional Aid," J.. Cji»m.. Ed^., 47, 97 (1970).

H. J. Karplus, (Ed), On Line Computing# McGraw Hill, 1968, pp. 131-78, 303-24.

j. Birut'U, uakruialaiiSA lacltu amius

J. a. Pople, B. g. sokneider and H.

aflaanaass* accratr mi, 1959, PP. 210-224.

K. J. Johnson, "Buaerioal Methods in Cheaistry— a Computer applications Coarse." J,

£kSls.£4s.> 47# 019 (1970). **■

P. Prosser and J. B. Moors, "Coaputer-Senerated lepeatable Tests in Cheaistry, • Proceedings

i«7ibe C0Bt#rBnce °“ Conpnters in Chenical Bdacation and lesearch, DeKalb, Illinois, July,
1# p« 9- 26-

101

112

113 102

Problem: Diminishing Polygon Forms

INTERFACING STUDENTS AND COMPUTING TH ROUGH
UNDERGRADUATE CHEMICAL RESEARCH

L. Chopin Cusachs and Lee P. Gary, Jr
Loyola University
Telephone: (504) 8bb-5471

Joyce H. Corrington
Xavier University
New Orleans, Louisiana
Telephone: (504) 48b-74ll

ABSTRACT

Computing as an avenue to early undergraduate research participation has been realized in
three different ways: (1) a rormal course in programming and numerical analysis, (2)
oart ici pa t ion in computer oriented summer research projects, and (J) academic year participation
in undergraduate research seminar courses* All three avenues have proved effective in an
informal program involving Xavier, Loyola, and Tulane University students and faculty. Benefits
to the students include the emotional and intellectual satisfaction of accompli shi ng useful
work, the discovery of talents and development of career interests, and co- aut horship of
respected original research papers.

Early involvement in research by undergraduates is easy when the attraction and teaching
potential of the computer is utilized. The possibility of using the computer to reduce the labor
of conventional calculations is well recognized, but the practicality of involving students at
the early undergraduate level in projects where the problem itself is computational, such as
molecular quantum mechanics or crystal structure determination, is little appreciated. The
organization of formal introductory computing courses to encourage a research attitude not only
provides a more interesting experience tor the students, but incidentally relieves the
instructor of muen drudgery. Both summer and academic year undergraduate research programs or-
ganized around com puta t iona 1 research have attracted strong student interest and proved
rewarding to both unusually gifted and more ordinary students. The following sections consider
introductory computing course organization and attitude, as practiced at Tulane and at Xavier by
two of us, and the summer and seminar undergraduate chemical research programs as developed over
the past few years at the three schools, Tulane, Xavier and Loyola Universities.

Formal Introductory Commuting Course

First contact with the computer for many students is the course "Computer Analysis in the
Physical Sciences" taught by one of us (LCC) for a number of years at Tulane, and its
counterpart at Xavier, "Introduction to FORTRAN Programming." These courses are adapted to the
facilities available at Tulane (an IBM 7044) and Xavier (an IBM 11J0). Each is open to all
students. At Xavier physical science and mathematics majors are required to complete the course.

We regard FORTRAN as a language to be learned by use, since a working or speaking rather
than a merely reading knowledge is of value. At the beginning we and the students discuss
familiar topics in computation, writing and suomitting programs to the computer with the first
meeting. As the semester progresses, the fluency of the students increases and the material
presented is less and less likely to be familiar to the student, but increasing expertise in the
language makes the gradual shift of effort from communicating with the computer to anticipating
sources of error seem natural.

A full outline of the course "Computer Analysis in the Physical Sciences" is included in
Appendix A. The basic attitude is to start with input/output and progress to numerical methods
of increasing sophistication. Each student, in consultation with the instructor, selects a term
project, and devotes approximately a quarter of the course effort to it. We have allowed a num-
ber of students to take a second semester as seminar or independent study. At the end of the
first semester, the average student has a functional command of FORTRAN and is capable of
writing programs in his work or research and usually even of adapting large or complex programs
from one type of computer to another. Since the large programs of quantum chemistry and X-r3y
crystallography are normally run in a batch job environment and the available larger computers
only operate in that mode, we adopt the batch job attitude from the beginning.

•Originally, the orientation of the course to batca job mode was simply making a virtue of
necessity. Once we accepted the necessity, we began to teach in ways that utilized the
inevitable turn-around time to encourage care, checking, and a measure of forethought. We

Introduction

iXi4

oeliove it is much easier for a student trained to think his programming in this way to adapt to
the convenience of terminals, higher level programming languages, etc., than the reverse.

The variety and the guality of the term projects completed shows the considerable potential
of this technique for involving students, even beyond the physical sciences students for which
it was designed. Project subjects ranged from the oovious, such as automated grading programs
and ecological dynamics to outside interests, such as one to transpose music and another (to
devise mi nimum- travel bussing plans for a hypothetical public school district.

We followed the suggestions of firs. Pary Irvin of the Tulane Computer Laboratory and of
Wilson T. Price, author of "Elements of Basic FORTRAN IV Programming," beginning with
input/output to place students on the computer in the first class period. A pleasant
consequence oi this approach is that the papers we received for grading are almost entirely
computer output, whicn is much more readable than our own handwriting, at least. This also made
it possible to adopt the policy that a student program that is acceptable to the computer, i.e.,
produced no error messages, and operated correctly with the data supplied by the instructor, is
correct for grade purposes.

Hesea rc h Programs

The rirst undergraduate research student in what was to become our inter-university group
sought out one of us out of curiosity about, the computer. The computer in the area at that tile
was an IBM 1410 at Tulane, and this student quickly mastered its FORTRAN capabilities and
proceeeded on to its assembly language and a few tricks like simulating a chain monitor by
placing several absolute programs on a tape in succession and loading from the console with an
assistant at the tape drive. The tear that such familiarity with the computer light drive
students out of tae labs quickly dissipated when this first student and his successor went on to
graduate school in pharmacology and physiology, respectively, preparing expenaental
dissertations, though it must be admitted that the first attached a mini-computer to his
apparatus to control the instrument and collect data more efficiently.

The next student was encountered in his freshman year as work-study labor for a funded
project. It was noted that he began to catch errors in coding assigned to him to keypunch; he
had become curious enough to take an informal, non-credit FORTRAN course at the Tulane Coaputer
Laboratory. He collaborated in the writing of programs of increasing complexity, achieving co-
authorship of papers in quantum chemistry when he discovered his calling: crystallography. At
last word he had completed his doctorate and was working on structure deter ainat ion on some
biological systems. At this point it became apparent that undergraduates could do useful
research in quantum chemistry and actual recruiting of research students was begun.

There are two clear advantages to doing research in theoretical chemistry and related
fields with undergraduates. First, they are not convinced that the subject is too difficult to
master with a little effort. Secondly, it turns out that programming and carrying out
calculations is a good way to learn the theory. Particularly for the curious student, the idea
of finding out what happens when a particular term is left out or approximated in one way or
another by actually doing the calculation several ways has genuine appeal. For the research
diLoctor on a tight budget, they can also be ine xpen si ve-bu t productive. There is also a
potential for encouraging graduate students to greater effort, particularly when an
undergraduate known to be only a B + student in other courses is able to lecture in a graduate
course, citing his own work once or twice for good measure. The effect at Xavier Univeristy has
been to make Chemistry the largest departmental computer user accounting for JO* of all acadeaic
use.

» ormal avenues to undergraduate research participation include the standard "senior"
research seminar courses encouraged by most departments when not specifically required, and
summer programs such as the NSF Undergraduate Research Participation Program.

The standard senior research seminar course is probably the least effective. By the senior
year it is usually too late # do much for the undergraduate. Getting started in research takes
most ot a year, and the sen* tends to be already looking beyond graduation to graduate school,
job, or service elsewhere. The freshman or sophomore is better able to spend the long hours
required to get started without hurting his regular academic performance. We find the grades ot
freshmen or sophomore research students in unrelated courses tend to rise when they get involved
in research - wh i le senior research generates distractions. The senior may actually be learning
much that is valuable, but he usually is too rushed to produce results commensurate with the
time his supervisor invests. When the student starts early in his career, he has time to learn
from others auead of him and to pass on some of his knowledge to his juniors. The feeling ot
participation in a small group with a real purpose often helps the shy or uncertain student to
mature socially as well as intellectually. Por these reasons we stress the desirability of
introducing students to research early in their undergraduate years.

104

However, with the assistance ot previously accumulated subroutines and calculation programs
even seniors with no previous computing or research experience can complete a worthwhile
projection a single term. One of us (JHC) supervised two such students in the spring ot 1971,
and each student completed and presented a paper on his work at a local Aiencan Chemical
Society meeting.

The intensive summer programs are particularly valuable but depend usually on outside
funding for student stipends to attract participants.

Professor L. P. Gary of Loyola, under an NSF-URP grant, supervised two students ana
Processor Joyce H. Carrington ot Xavier, under an ACS-PRF Type D grant, supervised six students
in the summers ot 1970 and 1971-

In addition to the obvious advantages of full time effort in research, the summer research
student can make a commitment for a specific period in an area of research and change in the
following year without having to explain to a disappointed supervisor why he really prefers, tor
instance, crystallography to quantum chemistry. The practice, in our group, of encouraging
students to try other research areas and other institutions tor a summer to sample some ot the
oth»‘r interests available has produced some switches out of our research group out provided a
better overall educational opportunity tor the student.

Project (Appendix U) orfers to summer and to academic year research students range from the
development of better programs and computational algorithms to the more applied study of
families of molecules or reaction systems to determine how well the methods account for the
physical and chemical properties of the systems. As examples, Benes Trus and C. W. McCurdy
worked on approximations and computer programs for molecular orbital calculations and the
computation of transition moments and transition energies for electronic spectra. It is
interesting that McCurdy discovered a manipulation to simplify calculation of electronic spectra
that was almost simultaneously noted by two established investigators at distant institutions.
As programmers there is no reason to believe that undergraduates should be inferior to their
faculty supervisors it they got enough practice. We should stress that participation in
undo rg rad ua te research in our group implies no commitment to our field after graduation; an
example is the work of J. £. Florey on pseudorotation in PF5 , which aid not conflict with his
plans for medical school, preparing for a career in psychiatry. A selected list of publications
involving major contributions by undergraduate research students is included (Appendix C) .

The one area in wnich undergraduates have been of little help to us is in writing the final
manuscripts ror publication. Had this not been the case, the list ot publications would be much
longer. However, some of the students did prepare an undergraduate thesis in tuliillient of the
requirements for an Honor Degree.

Tnoy have actively prepared slides and presented papers at local ACS meetings. At the 1970
Now Orleans ACS Meeting in Miniature students collaborating with the authors presented ten of
the fifteen papers accepted tor the Physical Chemistry Session. The papers are listed in
Appendix D.

ACKNOWLEDGMENTS

The work discussed in tnis paper was supported in part by; The Xavier Computer Center, The
Tul^ne Computer Laboratory and the Loyola Computer Center, and by grants from the American
Chemical Society Petroleum Research (Grant PRF-5056) , the Edward G. Schlieder Foundation and the
National Science Foundation.

APPENDIX A

"Computer Analysis in the Physical Sciences0

A. Concept of Course: FORTRAN is a Language, Computer Techniques tne Subject.

1. The course builds on one year ot college mathematics and one year of a course in
natural science.

2. batch Mode, typical of actual installation practice, is employed.

3. Assignments stress achievement of a functioning program, rather than caution to avoid
errors penalized in grading.

4. Individual projects challenge gifted students while the average one solidities his
com pe tence.

A language is taught by uss, a technique by analysis and sxperisentation
Courso parallsls actual ass o f cosputsr for real problsss.

Organization ot the Course: sequence of assignments.

1. Two lecture/laLoratory seetings per weak, plus instructor's availability outsids of
class.

2. Material for grading, with ons exception, is cosputer output; fast F0BTR4N (WATFOI)
cospiler keeps cost of ties acceptably low (less than S20.00/student at Tulans;
iSO.OO/student at Xavisr).

1. Early establishsent of Studsnt-Cospilsr dialogue helps student know where; hs stands,
"If it works correctly with the instructor's test data, it is correct. * Workab/ . with
inexperienced instructor, "Try it and sse if it works."

4. Stress on assignsents due on tiss over the sesestsr sinisiz os conflicts with

traditional courses at exan tisss.

Sasple Schedule ot Assignsents.

1. Keypunching and Control Cards (ungraded), READ, WRITE, FORMAT.

2. Elesentary Arithsetic in FORTRAN (ungraded) Integer, Real Arithsstic.

3. Construction ot a Table of Values of a Polynosial, DO Loop, Arithsetic Statsssnt
Function.

4. Roots of a Polynosial by Half- Interval Method (Reggla Fa jail ip statesents, Indexisg,
Modulo arithsetic. Arrays for data storage.

5. Roots of a Polynosial by Newton-Raphson sethod. Convergence of iterative processes.
Debugging tactics.

6. Hoots of a Transcendental Equation (optional) , Library functions.

7. Vectors £ Matrices (graded hand assignsent) , fundasontal definitions and
sanipulations.

8. Vectors £ Matrices, sanipulation in FORTRAN (ungraded).

g. Linear Equations, Gauss-Jordan elisination sethod. Indexing, More indexing.

10. Least Squares, Subroutines, COMMON.

VI. Nuserical Integration, Sispson's and Trapezoidal Rules, Gaussian Quadrature Forsulae,
Rounding vs. truncation error.

12. Ters project: Valued at 3 regular assignsents.

13. Optional, Ungraded, Eigenvalue Probles in Won-Orthogonal Basis, Nonlinear Regression.

14. Optional ventures in COMPLEX, and Double Precision Arithsetic, or Boolean Algebra — it
the cospiler is up to it!

Precautions £ Variations.

1. The ringer with sose prograssing experience— use as tutor at beginning if
cooperative.

2. The gifted student — encourage side explorations and retinesents.

3. The slow student — leave open a straight, sisple road.

4« Selection of Project "by negotiation."

a. Established interest of student, research or other.
b« Prograssing ability of studsnt.
c. Scientific or other talents of student.

106

C,m

5. Tune requirements - at Tulane, typically about 7 hours o t IBM 7044 time tor 2b

students. At Xavier about 30 hours o £ IBM 11J0 time tor 110 students.

Optional Second Term

1. Seminar organ izat ion ... the student is ready to read.

? F.

2. Theme. .. some t hi nq lixe difterential equations and the atomic self-consistent Hold

problem.

4 .1 use urn ot Student Programs and Projects (Appendix B)

APPENDIX B

Sample of Student Term Projects

Pupil Assignments to Minimize Busing (Social Sciences): A model ot a school district with
non-uniform racial and socio-economic populations and school building distribution. Compute
assignments to minimize the overall busing required for balance.

Titration Simulation (Chemistry): Specifying an amount ot base in known volume ot solution
and concentration and drop size ot standard acid, simulate the addition ot successive drops
of acid to base, computing pH and other ion relations, does not attempt to reduce to
quadratic or linear approximations.

J 3.

Comparison of Stability and Efficiency of Numerical Treatments ot DittecentiaL Equations; 1

Compares several popular numerical techniques with respect to stablity and computational
et f iciency.

Long Term Regulation of Extracellular Fluid and Arterial Volume by Control of Urine Output
(Physiology) : Digital implementation of a model of fluid balance factors m a living
system. Userul to test responses to various disorders or insults.

Statistical Package tor Quantitative Chemistry Lab (Chemistry): A simple but useful

statistical program package for the more frequent laboratory calculations m quantitative
analysis.

Nuclear Shape Calculations (Physics): Calculations using modifications ot fluid drop model
to estimate shapes of heavy nuclei of atoms.

Heat Transfer in a Square Pipe (Physics): The heat transfer in an ordinary circular pipe is
a standard textbook problem. A square pipe is interesting, useful, and messy enough to be
natural tor a computer.

Prediction of Power Diffraction Patterns (Crystallography): Computer prediction ot power

X-ray diffraction patterns for a specified assumed crystal structure.

A 3-d imensiona 1 Plotter Program for the Line Printer: Attempt to represent J-d imensiona 1

data on a two-d imensional line printer.

10.

Solution ot the atonic radial Schrodinger equatiou with Thomas-Fermi or Thomas-Fermi Dirac
Potentials (Physics).

APPENDIX C

Typical Publications Involving Major Contributions by Undergraduates

"Pictures of Molecular Orbitals" H. B. Becker, E Lon genecke r , Jrr, and L. C. Cusachs,

Communications of the Association for Coaputing Machinery 8, b81(19bb).

"Calculation of Molecular Transition Moments" L. C. Cusachs and 3^ L.. Trus, Journal ot
Chemical Physics 4o, 1S32 (1967).

"Selection of Molecular Matrix Elements from Atomic Data, III." L. Cusacns and J. K._ Linn,
Jr^, Journal ot Chemical Physics, 46, 2919 (1967).

ERIC

107 Vjj; .

118

. - 1 ■ II

107

4. "overlap Matched Atonic Orbitals," L. C. Cusachs, D. G. Carroll, and S. P. McGlynn,

Trus, int. J. ot Quantum Chetn., Js, 423 (1967).

5. "Thermodynamic Functions from Kinetic Data: A Nonlinear APproacn," JU Kr Nichols, T. F.

Pa q ley , and L. C. Cusachs, Student Members Bulletin, AlCh K. , fl, 39 (1967).

6. "The Mechanism of tne Hydrogen-Iodine Rear tion at Low Temperatures," L. C. Cusachs,
Krieger, and CA McCurdy, J- Chem. Phys. , 49 t 3740 (196H).

7. "Conservation of Molecular Orbital Configuration in Chemical Reactions," L. c. Cusachs, M._
K r i_e<je£ , and C^ W. ^cCu r , Int. J. Quantum Chem., JS, 67 ( 1964).

M. "The 4s Orbital ot Sulfur," L. C. Cusachs, D. J- Miller and C. McCurdy , Jr., Spect.

Ltrs. 2, 1 41 (1969) .

9. "Analysis of Hydrogen Binding in Ammonia Dimers Using an LCAJ-MO Scheme," Aldrich,

C. Hasen Kamjj f , H • J. Lad^r, L. C. Cusachs, and L. P. Gary, Bull, Am. PhysT Soc77”IS# IJJb

7i97or:

1U. "Electronic Effects in th« Structure of Some Silver Iodide Complexes," Dy H. B. Jonassen,

C. Kl. McCurdy, Jr., L. C. Cusachs, G. 3. Ansell, and W. Go Finnegan, NWTC-TP 499b (August,

7970)*.

11. "Dipole Moments and Orbital Energies from ARCANA: A Se m ierapir ical Molecular Orbital

Calculation Program," J. ii. Corrington, H. S. Aldrich, C^ W._ McCurdy, and L. c. Cusachs,
Int. J. Quantum Chem., 5S in press.

12. "^implication of the RP A Secular Equation," by C^ McCurdy and L. C. Cusachs, J. Chetn.

Phys. 54, (1 971) .

1J. "Somie mpi r ica 1 Molecular Orbital Calculations: Pseudorotation in Phosphorum Penta f lou rxde ,"
ay J- D-. £l.o££I and L. C. Cusachs. J. Aner. Chem. Soc.

Note: Underscore denotes student.

APPENDIX D

Student Generated Research Papers for ACS Meeting

1. "Dipole Moments and Orbital Energies from Arcana," S± Aldrich, Wt McCurdy, and L. C.
Cusachs.

2. "Simplified Calculations of Atomic and Diatomic Integrals," Jennifer Chr lstopher and Joyce
ri. Cor ring ton.

3. "An LCAO-MO Study of the 1, 2-Dihalogenoe thy lene Series," Keefer, L. p. Gary and L.

C. Cusachs. ~ ~

4. "Molecular Orbital Studies of Neu rot ransait ters , ” D;_ Burton, Jr.., and Vernon B.

iaarstad . ’*’**’*""

5. "Electron Finding in Azomethane," Hasenkampf and S^ Tr K,ent.

6. "Structure-Bonding Studies of Heoicholinium HC-3," Andrew Gr Pattamana and Joyce H.

Corrington. *

7. "Application ot the Random Phase Approximation to the Seaiempirica 1 Molecular Orbital.

Calculation of Electronic Spectra." fi££urdy and L. C. Cusachs.

*3. "A Study of the s t r uc t ur e- Ac tivit y Relationships of 1, 4- Benzod iazepines Based Upon

Molecular Orbital Calculations," tjyrphy , a.. Guerrero- Fig ueroa_, D.. Ga 11 anS J, L. C.

Cusachs. ~ ~ ~ ~

9. "Semienpirical MO Calculations of Model Systems for Drug Receptor Complexes; Methylamine

and Acetic Acid," Milton Coleman and Joyce H. Corrington.

10. "Triplet-Triplet Interaction Between Carcinogenic Aromatic Hydrocarbons," Hr S * Aldrich and

L. p. Gary. ~

Note: Underscore denotes student.

108

A CAI PB3GRAH FOB AROMATIC ORGANIC SYNTHESIS BRITTEN
IN TIME SHARING FORTRAN

Ronald D. Crain
University of Kansas
Lawrence, Kansas 66044
Telephone; (91 3) 864-4097

A beginning student in organic chenistry usually gets very little understanding of
syntheses until the benzene ring and its chenistry is introduced into the lecture naterial. At
this point the students begin to learn that all one does is introduce, alter, and renove groups
uoa a fixed ring systen according to certain defined rules. In fact, this type of synthesis is
referred to as "tinker toy" because the ring can be viewed as a constant fraae of reference.

Probleas are noraally assigned for homework and the lecturer covers in class the general
approach that should be followed by the student. The answers finally get posted and the student
has a chance to discover which ones he nissed. The better students are often able to innediately
see where they went wrong but aost students wonder why a particular synthesis was incorrect and
what step was wrong. Unfortunately, the answer can often be that they were not aii wrong but
that they siaply had not taken the standard route. This can be clarified for the student if he
talks with an instructor. Ip a large institution this is guite difficult because there are too
many students and not enough time to help everyone requesting the additional help.

One of the obvious approaches for such logistical probleas in teaching is to develop a CAI
program to handle the aajority of the student's need for confiraing which synthetic steps, and
in what seguence, are feasible for aaking a coapound. It would be far easier to write a prograa
which requires that a student begin with the starting naterial and proceed stepwise to the
product. However, that is not the way an organic cheaist would approach the problea. One starts
at the end and does the last step first. Occasionally you jump to the beginning and take the
starting naterial one step forward and coapare it with possible routes to the other end. Thus,
to be pedagogically correct an organic synthesis CAI prograa would havo to have this
versatility.

There have been several prograas produced for synthesizing organic benzene conpounds. Dr.
Stanley Saith, University of Illinois, has reported^ 1 ] on the use of their PLATO systen for such
purposes and Dr. L. 3. Rodewald and coworkers[2] at the University of Texas have several
completed prograas in this area. To the best of the author's knowledge none of these programs
allow a student the privilege of starting anywhere along a reaction path.

Such a program has been written in tine sharing PORTRAN for use with the HU-636 computer at
the University of Kansas which atteapts to neet with this reguirenent. In addition, this program
should have a relatively easy transferability to other computer systeas since standard teletype
or CRT terminals are used and the progranning language is slightly modified PORTRAN IV.

Prggcaa Use

A student is given a sheet of paper which describes how to call the program at the
terainal, a list of reagents which can be used, and a list of substi tuentss which could be
attached to the ring (or removed). The present program can utilize up to three substituents on
the ring at any given tine (sea Table 1), thirteen different substituents, and 24 reagents. The
chenistry of the aliphatic sida-chains, other than oxidation, ~ not included in the program.

Probleas can be assigned by the instructor or the student aay use those in the text or nake
up his own synthesis problea. Upon entering the prograa (Pigure 1) the benzene ring is printed.
Tha student aay either start with the benzene or add substituents , up to three, for his first
reaction, suppose he added a CH3 in the 'one' position. The structure of toluene is printed and
the student is asked to enter the reagents to be used. The major product froa the reaction is
printed ant the student has tha option to continuing the synthesis to a third compound, getting
a nsw starting material, or guitting. Le-'s assume that he has nitrated and now bus 4-
nitrotoluene as a product (Pigjre 2) • If potassium dichroaate and sulfuric acid are chosen, 4-
nitrobenzoic acid's structure is printed. If tin and hydrochloric acid is used the structure for
4-amino-toluene ( p-toluidine) is printed at the terminal. Reaction of the aaine with an
oxidizing agent will result in a message being returned that this type of reaction gives a
terrible aixture. The student is then offered a chance to try soae other reagent (s) .

There are features of this program which have helped the student become familiar with the
technigues needed for a successful synthesis problem. The presentation of all of the reagents
(tools) in one place allowed the student to get a different perspective on the use of these
conpounds in synthetic work. It has helped to reorient their thinking from the concept that each
step is a new one reguiring antirely different and unrelated chemicals (a common misconception

l£0

'• r

109

HC CH

I I

HC^ /C\\

WHAT SUBSTITUENT IS NEEDED?
"CH3

WHICH CARBON ATOM?

-1

WHAT SUBSTITUENT IS NEEDED?
* (carriage return)

Ft*

HC CH
I I
HC CH

WHAT REAGENT DO YOU WANT?

/\5
HC CH
I I
HC^^CH

CN02

WHAT REAGENT DO YOU WANT?

S'.t

ANYTHING ELSE?

-HCL

/CCH5

CNH2

.CH

WHAT REAGENT DO YOU WANT?

-K2CR207
ANYTHING ELSE?

•H2S0V

THE AMINE GROUP OXIDIZES

IT IS VERY MESSY SO TRY SOMETHING ELSE

WHAT REAGENT DO YOU WANT?

FIGURE 1. Selection of starting material.

FIGURE 2. A typical program printout.

DATA BENZ/

f II II II It

It It

11 11 n 1

II l| *1 l|

II <1

11 it it t

It II II II

II II II II

it ti it 1

II II II It

II II II II

m 11 it •

II II *1 II

,MHM*

„ „*.,Hf

II II • 1 >1

III

f»C\

11 m it£i

II *1 II II

.. M M/-.

11 11

II M It 1
•

lt\ II II II

llQll II II

it 11

11 it 11 f

II It <•£"

"H" *”\ "

11 11

•i 11 11 >
»

|,7,\mh,\

II It || It
»

/•c”!

It Jll II £l

11 11 it ti

111

II II II It
*

, "H"*

II H ll^jl

11 11 11 ti

II II II It

11 n

II II II 1

11 11 n it

II It II II

11 11

II II ll 1

11 11 11 it

II It It II

11 11

II II II 1

11 11 11 H

II II It II
1

11 11

It II II 1
»

n 11 »i n 1

DATA FUNC/"HM,,,C",MN,\"B"f ’'C’V’rV’OVN'V’N'y’N'Y’C'V'C'Y’S’V'A'V’ ”,

” M f "H” , ”HM , ,,RM , "L11 , 11 M

M It lltll » * A * t II II II H II If || || IIOII lipil If/-*'1 HO II II II 11*11 II II || ||

» > » n » » » » | C I C I ^ | C I , J > f ,

M •• • • 11 npn 11 11 11 11 11 11 11 11 11 it it 11 1 1 t 11 iiuii 11 •• nuii n 11 11 11/

» I U I » » » » » » ^ , ft , »**» t f

FIGURE 3. Data storage arrays BENZ and FUf for structural manipulations.

ERLC

110

1S£

la changed to

„A,

I I
HC^ ^CCL

HC CN02
I £
^CH

►

PIOURE 4. Chaining a structure stored in BENS .

Reagent • Available

HNOg

FeBr3

KaCraCV

h2so4

FeCl3

KMn04

Hri

AIC13

NaNOa

C02

Br2

CuBr

ACgO

Cl2

CuCl

AcCl

CuCN

NaOH

CHg

Allowable Croupe
Br

no2

vh2

QAc

h2ci

NHAc

co2h

SC3H

TABLE 1 . Reagents and substitutes for Aromatic Synthesis program.

122

with beginning students) to be nemorized. The students have the freedom of checking out a given
compound with a given set of reagents without even having a synthesis in Bind.

The not-so-good features are mainly due to the limitations of a standard teletype terminal.
The printout rate is 10 characters per second thereby Baking the construction of a two-
iiaensional molecule a little bit lengthy (slow). The steps in the synthesis are also printed in
a vertical fashion rather than the standard approach used by text, teacher and student:
(horizontally). At the present time no attenpt has been Bade to save, upon coaaand, a given stop
and then print out the entire completed synthesis when the student is satisfied that it is
correct. There is also no atteipt to check the last compound produced in the synthesis to see if
it agrees with what the student set out to lake. These features are nice but the program could
becoae quit'a lc.rge for nany systems and then a loss in transferability occurs. (They are being
iacluded, when time permits, for our own internal use).

One slightly bad pedagogical item should also be mentioned since the program as presently
constructed makes no mention of a chemical reality. Quite often there are two possible products
obtaiucd from a reaction. This program gives only the major product. The inclusion of the
student option of picking one of two possible products is being studied but it may weJ 1 be
somewhat dependent upon special display units (CRT) which in turn would make the transferability
of the prograa more difficult unless the user also had a similar terminal.

The internal working of the program is guided by one da^i array (two-dimensional) in which
the structure of the benzene ring is stored in character fora (Pigure 3). Alterations to this
structure are dictated by the reagents selected and any other groups that may be present, for
example, if the reagents selected dictate the placing of a nitro (NCK) group on the ring the NC>2
is read from the data array FUNC into the benzene data array (BENZ) starting at a specified
point in the BENZ array. The same thing could have been accomplished by having the student
select a nitro group and reguest that it go to the 'one* position. A simple print subroutine
then prints out what is stored in BENZ as a two-dimensional molecule. The BENZ and FUNC arrays
are set up in ASCII A1 fields but that is not necessary. Routines have been done where the same
type of thing can be done using A2 or A4 fields.

There is a second routine which can check the BENZ array for the type of substituent and
where it is located. If there is nothing on the 'one* carbon atom (see Pigure 4) other than a
hydrogen atom and a group is found on the second or third carbon atom then the program redoes
the structure so that the group appears on the first carbon. This was included in the program to
reduce the actual number of statements to handle the rather large variety of possibilities. If
one has a compound like 1 , 2-dicn lorobenzene it is actually the same as 3,4-dichlorobenzene (or
2,3- or 4,5-, or 5,6-, or 1,6-). Thus the variation is reduced by a factor of six in this one
instant. In t.Ue latter cases they would all be translated in the BENZ array as 1,2-
dichlorobenzene and printed as ruch.

The same routine can also determine the branching in the program where the chemistry of {!)
benzene; (2) non osubs ti t uted benzenes; (3) 1 , 2-disubsti t u ted ; (4) 1 , 3-d i subst it u *:ed ; (5) 1,4-
disubs tituted; *>) 1,2,3-trisubst ituted, etc. This allows the student to build a benzene ring
with up to three substiturnts on it or actually make the compound during a synthesis and this
pro*: ;am would check out the molecule, shift the groups if necessary, and branch to the area
where the chemistry of that type of substituted benzene is covered.

112

AH INTERACTIVE TIBE-SHARING BASIC TUTORIAL PROGRAM SEQUENCE
IN INTRODUCTORY ELECTROCHENI ST HI

Alfred J. Lata
University of Kansas
Lawrence, Kansas 66044
Telephone: (913) 804-4054

In an effort to assist our General Chemistry students in and through those areas of the
course which are perennially Jifficult, we investigated the possibility of utilizing Computer
Assisted Instruction (CAI). However# the University of Kansas does not have a CAI language such
as Coursewriter or PLANIT# or a system such as PLATO available. Efforts to convince our
Coaputation Center staff to adopt and/or develop a CAI language have fallen on sympathetic ears.
The Center’s feeling# however, was that with only one coaputer available (a Honeywell 6Ji>) and
with our software facilities, a lengthy period of tine would be necessary to adopt and aodify
one of the existing CAI languages, and the aaount of aeaory necessary would aean that the
coaputer would have to be dedicated to CAI, to the exclusion of general use. We were advised
that if we wished to do any CAI work within the next one to two years at least, we would need to
use existing facilities.

He were, and are, therefore in the saae situation as aany other schools throughout the
country. He soon recognized the fact, however, that if we were able to write effective CAI
prograas in TSS BASIC and/or TSS FORTRAN, these prograas could be used by other schools on their
own coaputers without the need of their having a CAI language available. Hhat we had thought a
handicap, has proved to be instead an advantage, in that these prograas will be readily
transferable.

He have now written and tested CAI prograas in TSS BASIC and TSS FORTRAN. Ihe prograas

probably take longer to write in these languages than in a CAI language, but they also work

effectively with students. He have used both CRT and teletype for output, the latter being aore

desirable since the student has hard copy for review. The fact that there are no lover case

characters or subscripts is a ainor problem that is easily overcone by the students. As evidence
of their transferability, several of our prograas have been taken to other schools and with
ainor aodif ications have run on their coaputers.

To show a portion of what ve have achieved, I wish to discuss a group of computer assisted
instruction prograas written in tine-sharing BASIC covering topics in beginning Electr ocheaistry
commonly discussed in a General Chemistry course. There are seven prograas:

1. REDOX is a program designed to teach students the ion electron nethod of
balancing of redox equations assuaing no previous experience.

2. REDOX2 allows the student to practice balancing redox reactions by the ion-
electron nethod at either, or both of two aore advanced levels than the
previous prograa.

3. CELLCALC: the student calculates the potential of a cell fron two reduction

potentials. All concentrations are 1 nolac.

4. STDCALC allows the student to find the potential of a half cell given the whole
cell potential and the potential of a reference electrode to which the half
cell in question is coupled.

5. NERNST : the student deternines the potential of a half cell it the

concentrations of the ionic species in the half cell are other than 1 aolar.

6. COMCpQT has the student find the concentration of an ionic species given the
potential of the half cell.

7. COMPCALC is a progma in which the student is given the potential of a cell,
coaposed of a reference electrode and a half cell with either a saturated
solution or a solution of a coaplex ion whose KSp or K^^ss the student
determines.

The random number generator function was used in all prograas to select data, both

equations and numbers, for the st» cent’s problem; this means that the probability of two

students getting the identical problems or equations is snail. There are few fixed answers in
any of the programs, answers being calculated by the computer and the student’s answer then
compared with the calculated result. The student is asked to respond to a guestion or problem.

If his answer is correct, he may choose to go on to another problea or the next step. If the

113 ^*54

answer incorrect, he is either given a diagnost'c response and/or told to try again, or he is
asked to respond to a question dealing with the innediately previous step in the calculation, by
which it nay be possible to determine the student's error and gire bin a diagnostic* This
retrograde questioning continues until the student's error is located*

The student has the flexibility to get oat of a probien by responding "99" or "out" to a
question, or to seek assistance by siapiy typing "help" to find out the answer to the previous
question; this is done by a subroutine which examines each answer for one of these responses*
Because of a floating point conversion probien in coaparing student nunericai responses to
conputer generated nathenaticai solutions, each student nathenaticai answer is exaained to
deternine whether it is within an allowable percentage range; this percentage existing in the
progran for each calculation*

I wish to discuss the prograns briefly, stressing particularly th^ prograas used first in
the progran sequence — REDOX and REDOX 2, which are non- nathenaticai in nature; CELLCALC will be
used to illustrate the renaining prograas to give an idea of how nathenat ically oriented
prograas function in this group* Ail prograas were originally written as integral prograas to
stand alone; however, several subroutines are connon to several prograas and are now called up
frou the file when needed*

The initial probien to be solved in developing the progran REDOX, was to code the data
sta^aents in order to have available for each half reaction the reacting species, products, the
nuaber of hydrogens and oxygens in each species, the nunber of electrons for the half reaction,
and whether the reaction takes place in acidic or basic nediun* The reduction half reaction

H3As04 + 2 H+ + 2 e- - UAs02 + 2 H^O 0.56 Volts

is coded in the following fashion for the BASIC data statement*

1 H3AS0U k 3 2 1

A B C D E F

A = # of H3As04 in equation
B = oxidizing agent
C = # of 0's in oxid. agent
D - # of H's in oxid. agent
E = # of electrons

K « 1 for acid, 0

HAS 02 2 1 0.56 1

G HI J K

F = # of HAsO^ in equation
G = reducing agent
H = # of 0's in reduc . agent
X = 4 of H's in reduc. agent
J = Potential of half cell
>r neutral, -1 for basic

The data available in the prograa are 34 reduction half reactions (including two organic
reductions) arranged in order of decreasing reduction potential* Two half reactions are
selected by use of the randoa nuaber generator* The pair is exaained to check whether acid-base
coapa tibility of the two reactions is observed by coaparing the values K, the last value in the
data stateaent* If the half reactions are incon patible, one of the reactions is replaced by
another randonly selected half reaction. In our current file of 34 half reactions, 22 are in
acid solution and 12 are in base: this gives 231 possible whole cell equations in acid, and 66
possible in basic solution* If all half reactions were in acidic solution, there would be b61
different possible whole cell reactions that could be atteapted by the student* After the
student signs on and selects progran REDOX, he is given sone introductory infornation and then
the unbalanced equation is given bin*

MNOU- + FE+2 - MN+2 + FE+3 IN ACID SOLUTION

or BR0- - BR- + BRO}- IN BASIC SOLUTION

THIS IS A DISPROPORTIONATION REACTION

or CLOU- + CL02- - CLO^- IN BASIC SOLUTION

125

114

It is only in the initial equation that the disproportionation or the single product is shown.
You will note that one of the reduction half reactions has been reversed to show that oxidation
is ' taking place. This is performed internally within the progran* shown here is a portion of
the beginning of the progran, renenber that this is an introductory elenentary balancing of the
redox equation.

The progran is capable of handling equations in either acidic or basic nediun. The nunber
of oxygens, hydrogens# and waters needed in the equation are calculated fron the nunber of
oxygens and hydrogens in the oxidized and reduced species: each excess oxygen on the left
requires two hydrogen ions and forns one water in acid solution; or in basic solution# each
excess oxygen on the left reguires one water and forns two hydroxide ions. In acid solution# if
there are nore hydrogens in the reacting species than in th<? product, this decreases the nunber
of protons needed on the left, e.g.#

H3As04 + 2 H+ + 2 e“ -* HAsOe + 2 H^O

There are two excess oxygens on the left [ • of 0 • s in oxidized forn (4) - i of 0's in reduced

forn (2)]# and the two excess H's on the left [calculated in the sane uanner# (3-1]# reduce the

nunber of protons needed on the left to two. sinilar calculations are perforaed by the conputer

for reactions in basic nediua. A portion of the progran is shown here:

LET’S BALANCE THE EQUATION:

CR207-- + HAS02 - CR+3 + H3AS04 IN ACID SOLUTION

WHAT SUBSTANCE IS BEING REDUCED?

?CR207“~

WHAT SUBSTANCE IS BEING OXIDIZED?

?HAS02
GOOD, JOHN

FOR THE REDUCTION HALF REACTION CR207-- - CR+3 YOU

WILL NOTICE THAT ONE CR207-- GIVES 2 CR+3 TO BALANCE
THE NUMBER OF ATOMS OF THE ELEMENT BEING REDUCED

WHICH SIDE HAS MORE OXYGENS?

?LEFT

CORRECT, JOHN! HOW MANY MORE ARE THERE ON THE LEFT SIDE?

;l4

TRY AGAIN, JOHN

RIGHT, JOHN!

HOW MANY WATER MOLECULES WILL THE OXYGEN FORM?

VERY GOOD, JOHN 1 CR207" - 2 CR+3 + 7 H20

THIS WILL REQUIRE HOW MANY H+’S ON THE LEFT?

NO, REMEMBER THAT EACH WATER GIVES TWO H+ IONS.

TRY AGAIN

?l4

The student goes through both the oxidation and the reduction half reactions in this nanner
and then he deternines the least coanon multiple of electrons for both half reactions

1 HAS02 + 2 H20 - 1 H3AS04 + 2 H+ + 2 E-

NOW LET'S COMBINE THE HALF REACTIONS. THE REDUCTION
HALF REACTION WAS:

1 CR207 — + 14 Hf 4 6 E- - 2 CR+3 + 7 H20
WHAT IS THE LOWEST COMMON MULTIPLE NUMBER OF ELECTRONS

COMMON TO BOTH EQUATIONS?

?12

►

NO, JOHN, WHAT IS THE LEAST COMMON MULTIPLE OF 2 AND 6?

RIGHT! HOW MANY OF THE REDUCTION HALF REACTIONS DO YOU
NEED TO TAKE UP 6 ELECTRONS?

couples the half reactions, and determines the number of each species on both sides of the
equation,

THE SUM OF THE TWO HALF REACTIONS IS THEN:

1 CR207— + 3 HAS 02 + 6 H20 + l4 B+ -
2 CR+3 + 3 H5AS04 + 7 K20 + 6 H+

WHICH SIDE HAS MORE WATER MOLECULES?

7RIGHT

HOW MANY MORE WATER MOLECULES?

GOOD. AND WHICH SIDE HAS THE GREATER NUMBER
OF H+ IONS?

?LEFT

HOW MANY MORE H+ IONS?

GOOD. NOW THE EQUATION SHOULD READ:

1 CR207-- + 3 HAS02 + 8 Hf -
2 CR+3 + 3 H3AS04 + 1 H20

In the program RED0X2, a different coding is used for the equation, and this coding is used
in all subsequent programs except COHPCALC.

For reactions in acid solution

the coding is:

1 HaAaO* + 2 H+ + 2 e“ HAs02 + 2 0.56 volts

1 H3AS04 2 2 1 HAS02 2 0.56 111

A B CEF G H JKLM

For reactions in basic medium

2 CIO" + 2 HsO + 2 e" Cl2 + 4 OH" 0.40 volts

the coding is :

CLO-

CL2

4 0.40

H J

-1

A - # of CIO" 's in equation
B - oxidizing agent

C - # of H+ if acidic
# of HgO if basic

E - # of electrons

K - 1 for acidic, -1 for basic
L for oxid. agent
M for reduc. agent

F ■ 4 of Cl2 in equation

G - reducing agent

H - # of HsO if acidic
# of OHis if basic

J • reduction potential

0 for solid,

1 for ion or soluble molecule

2 for gas

$Z7

116

This coding differs from that in the previous program in that hydrogen ion, or hydroxide ion,
and water are included in the data for each equation rather than the number of oxygens and
hydrogens in each individual species. Also at the end of the data statement a coding for solids,
ions or molecules which can vary in concentrations, and gases is included for both the oxidizing
agent and the reducing agent. In this prograa [with two levels of difficulty (1) balancing each
half reaction and then the whole reaction and (2) balancing only the whole final reaction] the
student deteraines how aany hydrogen ions (or hydroxide ions if basic) and waters are necessary
n each equation. A portion of this prograa is shown below.

BALANCE THE FOLLOWING EQUATION:

103- + H2S03 - 12 + HSOk- IN ACIDIC SOLUTION

BALANCE THE FOLLOWING OXIDATION HALF REACTION
H2S0J, -4 IISOU IN ACIDIC SOLUTION

ON THE LEFT SIDE: HOW MANY H2S03-?

HOW MANY WATERS?

HOW MANY H+'S?

ON THE RIGHT SIDE: HOW MANY HSOU-?

HOW MANY H20'S?

n *

HOW MANY H+'S?

HOW MANY ELECTRONS?

"HE NUMBER OF H+'S ON THE RIGHT SIDE IS WRONG *

iHE NUMBER OF ELECTRONS ON THE RIGHT SIDE IS WRONG.

BALANCE THE EQUATION AGAIN AND WE'LL TRY AGAIN.

(The equation should read H2S03 + H^ -4 HSO4" + 3 H+ + 2 e“)

After each half reaction is worked correctly in this fashion, the student then finds the
nuaber of electrons common to both half reactions, couples the two half reactions and then is
questioned in the same fashion about the final balanced equation.

NOW THAT YOU'VE DONE BOTH HALF REACTIONS, COUPLE
THEM AND I'LL CHECK YOU ON THE BALANCED EQUATION.

HOW MANY ELECTRONS ARE COMMON TO BOTH EQUATIONS?

RIGHT, JOHN, NOW CONSIDER THE WHOLE BALANCED EQUATION
ON THE LEFT SIDE: HOW MANY HSOU-?

In the second level of RED0X2 the student is given only the skeletal equation and must work
out the individual half reactions on his own with no computer dialogue and respond only about
the final balanced equation; this is evaluated as were the half reactions at the previous level
and if a mistake in the number of one of the species is found, the student is so informed and
sent back to resubmit the number of each species. An example is shown below.

■ ¥

1 1 7- >

128

YOU WILL BE GIVEN A SKELETAL REDOX REACTION TO BALANCE:

BALANCE THE FOLLOWING:

103- + H2S03 - 12 4- HSOU- IN ACIDIC SOLUTION

I'LL CHECK YOU ON THE BALANCED EQUATION-
ON THE LEFT SIDE: HOW MANY H2S03?

HOW MANY I03-?

HOW MANY WATERS?

HOW MANY H+'S?

ON THE RIGHT SIDE: HOW MANY HSOU-?

HOW MANY 12?

HOW MANY H20'S?

HOW MANY H+'S?

THAT'S RIGHT, AND THAT GIVES US FOR THE
BALANCED EQUATION

5 H2S03 + 2 103- + 0 H+ + 0 H20 -

5 HSOU- + 1 12 + 3 H+ + 1 H20

WANT TO TRY ANOTHER ONE?

In program CELLCALC the student is asked to find the potential of a cell made up of two
half cells selected at random from the table* The student should have the table of reduction
half reactions and potentials at hand since in only one of the three levels of this program are
potentials for the half cells given in the output* The concentrations of all species are
considered to be one molar* The student may initially choose which of three levels at which he
wished to start work; five successful problems at one level advances him to the next higher
level where the problems are slightly more difficult* In Level 1 the half cells are given with
the potentials:

CONSIDER A CELL COMPOSED OF THE TWO HALF CELLS:

(ALL CONC AS 1 M)

HSOU- + 3 Hf + 2 E- - H2S03 + 1 H20

WITH A REDUCTION POTENTIAL OF 0.17 VOLTS

103- + 12 H+ + 10 E- -♦ 12 + 6H20

WITH A REDUCTION POTENTIAL OF 1.20 VOLTS

IN ACIDIC SOLUTION

WHAT IS THE POTENTIAL OF THIS CELL?

In Level 2 only the half cells are given, the student must find the potentials from the table:

CONSIDER A CELL COMPOSED OF THE TWO HALF CELLS:

(ALL CONC ARE 1 M)

HSOU- + 3 H+ + 2 E- ^ H2S03 + 1 H20

103- + 12 H+ + 10 E- - 12 .+ 6 H20

IN ACIDIC SOLUTION

WHAT IS THE POTENTIAL OF THIS CELL?

< o

And in Level 3, the balanced redox equation is given and the student must decide which halt
cells and corresponding potentials to pick froi the table:

A CELL HAS THE CHEMICAL REACTION:

(ALL CONC ARE 1 MILAR)

5 H2S03 + 2 103“ + 0 H+ + 0 H20 -
5 HS04- + 1 12 + 3 H+ + 1 H20

WHAT IS THE POTENTIAL OF THIS CELL?

When the student responds with his answer it is compared to the answer calculated froi the data

given for the two half reactions, by subtracting the reduction potential of the halt cell

undergoing oxidation from' the potential of the other half cell. If the student9s answer does
not natch the computer calculated answer within allowable Units, his answer is then conpared
against other possible incorrect answers calculated using the nistakes nost connonly connitted
by students: (1) sinply adding the two reduction potentials; (2) reversing the sign of the

wrong half cell which will result in a negative potential which is not indicative of a

spontaneous reaction; and (3) nultiplying the potential by the nunber of electrons involved in
the change. Por any other answer, the student is quizzed as to what reduction potential he used
for each half cell. If it is found that one of these is in error he is told to go back and do
the problem again; if the reduction potentials he used are correct he is then told that, he
apparently made a computational error and to try the problem again.

The program STDCkLC is used to give the student practice in the calculation of a halt cell
potential from a whole cell potential in which one of the half cells is a reference cell whose
potential he knows. The initial question is given to the student in the following form:

FIND THE REDUCTION POTENTIAL OF THE HALF CELL
MN04- + 8H+ + 5 E- - MN+2 + 4 K20

WHICH WHEN COUPLED TO A SATURATED CALOMEL REFERENCE
ELECTRODE HAVING A REDUCTION POTENTIAL OF 0.249
VOLTS, GIVES A CELL GENERATING 1.45 VOLTS. THE
REFERENCE ELECTRODE IS THE ANODE.

In the problem three things are chosen using the random number generator: (1) the half cell in
question; (2) the reference cell; (3) the cell potential. The reference cell is designated as
either anode or cathode by comparing its potential with the calculated potential for the half
cell in question.

Programs NEBNS? and COkiCPOT utilize the tiernst Equation,

E = E0

.•252 lo_ Cmd]*

n 18 L0Xp*[H+]x

Again, the random number generator selects for the student a half reaction with which to work.
In program NEBNST, randomly selected concentrations are given for the chemical species and the
student is asked to calculate the potential of the half cell. In program CONCPOT the student is
given a potential for the half cell and asked to calculate the concentration of one of the
species [ (OX), (BED), or (H*) ], given the concentrations of the remaining species in the half
cell. As in the previous programs, percentage limits are set and possible incorrect answers are
calculated and compared to the student*s answer, so that if it is in error a diagnostic may be
given.

Program COflPCALC combines several of the previous programs the student is asked to
determine K^iss or K«p given the potential for a cell composed of a reference electrode chosen
at random and one of the half cells, containing either a complex ion or a saturated solution. He
must go through the process of finding the potential of the half cell; the concentration of the
ion in question using the Nernst equation; and, with the concentration of complexing, or
precipitating species, the equilibrium constant.

,130

A CELL COMPOSED OF AN ANTIMONY REFERENCE ELECTRODE

HAVING A REDUCTION POTENTIAL OF 0.145 VOLTS IS

COUPLED TO A ZINC ELECTRODE IN A ZN(NH3)4++ SOLUTION (0.1 M) .

THE EOUIL. CONC. OF NHJ IS 2 M AND THE POTENTIAL

OF THE CELL IS 1.2^9 VOLTS. THE REFERENCE ELECTRODE

IS THE CATHODE.

WHAT IS THE K DISS OF ZN(NH3)4-H-?

) Conclusion

i He believe that ve have written educationally effective tutorial programs tor
* electrochemistry in time-sharing BASIC, programs that can be oasily transferred to other
f computers. It is possible to write interactive CAI programs without a CAI system or language. We

are currently in the process of converting our BASIC programs to FORTRAN which aay allow for
still greater transferability. It is our belief that if individuals at various schools write
CAI programs in the more common languages and share these programs with other schools, effective
libraries of these materials can soon be created for student use at many institutions. He urge
you to join us in this endeavor.

120 131

MICROMOD: DESCRIPTION * DSE AND EVALUATION

OF A MICROECONOMICS COMPUTER GAME

J. William Hanlon
Winona State College
Winona# Minnesota 55987
Telephone: (507) 457-2051

Donald p. Cole
Drew University
Madison# New Jersey 07940
Telephone: (211) 377-3000

The purposes of this paper are (1) to describe Micromod# a computer game designed as an aid
to teaching intermediate microeconomics t (2) to describe sole of the mechanics of using
Hicri'nod# and (3) to report the results of an empirical study designed to answer soie questions
about the validity of using micromod as a criterion for determining the course grade[ 1 ]. This
question of validity is significant because grading provides the incentive for serious economic
analysis of micromod as it is played# but if high performance in micromod were not related to
competence in economics# one would certainly question the visdon of using it as a basis for
gra ding.

Microeconomics is that division of economics generally concerned with the individual and
collective behavior of business firms and consumers as they function to accomplish the
allocation of the resulting economic goods and services among consumers. Of primary concern is
the free market environment where the system of prices# free to respond to the actions of firms
and consumers# provides the network of communications that integrates these actions to form a
complete economic system. While microeconomics is ultimately concerned with the economy as a
whole# the great bulk of discourse in the field is concerned with analysis of small segments of
the economy as represented by theoretical models of firms and consumers set in alternative
economic environments.

The traditional approach to teaching microecomics at the undergraduate level is to study
concepts and relationships within the context of theoretical models# while attemptimg to
demonstrate relevance by pointing to examples taken from the real world. There are at least two
major shortcomings to this approach. First# it is extremely difficult to locate real-world
exaapLes that clearly demonstrate basic economic concepts and relationships. This does not mean
these concepts and relationships do not exist# but rather that they are obscured by many
extraneous factors# both economic and non economic# so that any single economic concept or
relationship cannot be isolated and observed. Indeed# the reason economists rely so heavily on
models at all is that the real world itself is ouch too complex to analyze directly.

The second shortcoming of the traditional approach is that the dynamics of the models may
receive little or ro attention. Primary concern tends to be toward constructing models and
describing equilibrium conditions# with little attention given to the behavior that causes a
model to move toward its equilibrium state# or to the states it passes through enroute to
equilibrium. Consideration of such dynamics would give the student a more complete and
permanent understanding of economic models.

Micromod was designed to remedy these two shortcomings of the traditional approach. First#
it provides a means whereby the student can directly observe the implications of a fev basic
economic relationships# just as the chemistry laboratory experiment enables the student to
isolate and observe relationships between certain chemicals in controlled and known
environment. Second# the student supplies the behavior# given certain goals along with the
environmental conditions specified in the computer program# that results in observable outcomes.
Specific behavior is readily associated with specific outcomes. The student is a part of the
processes of change and adjustment that occurs as the model moves toward its equilibrium state.
This hopefully results in a better understanding of these processes# and of economic models in
general.

Description of Micromod

Micromod consists of three separate games based on computer simulations of several
microeconomic models. Each game# pure competition# pure monopoly# and oligopoly# represents a
particular environment in which a product is produced and sold. Each environment is described
by a single equation built into the computer program. The equations are:

Introduction

121

Pure Competition: P « A + B( Sj^) + E( M^) + FR + HY
Pure Monopoly: Di « A + KV>i + WMj^ + FR + HY
Oligopoly: Di « A + B( Si) + KPi + E( Mi) + WM

inhere :

P » Market price

A - The intercept

i Si » Total amount of product supplied by all firms (students)
*Mi » Total amount spent on advertising by all firms
R = Price of a related product
Y = Per capita income

Di * Demand for the product of a particular firm (student)

Pi » Price charged by a particular firm

Mi * Advertising expenditures by a particular firm

All other symbols represent coefficients which can be changed from time to time in the
computer program, and which values may or may not be revealed to the students.

A fine for violation of antitrust laws is levied in oligopoly whenever the demand foe the
product of any firm is larger that 30% of the total output of all firms. This adds an element
of reality faced by real-world firms.

A set of five cost functions is included in each game. Each function includes three
equations, one for total cost, a second for average total and a third for marginal cost. Each
is of the form favored by the conventional microeconomic theory with zones of increasing and
diminishing returns. Each function is identified by its fixed cost.

Meclja n ics of Using Micro mod

Each student acts as a firm in each game, and is given a goal, such as to maximize profit
or to maximize market share. The decision variables, manipulated by the student, in pure
competition are the amount of product supplied and the level of advertising expenditures. The
decision variables in pure monopoly and oligopoly are these two plus the price charged for the
product. In addition, students must select which of the five cost functions to use for
producing in each game by specifying the level of fixed cost in each round of play.

Each game is introduced as the corresponding chapters are covered in the text. Eventually
all three games are played concurrently through the remainder of the course as other topics are
covered •

Each student's decisions are punched on a computer card, one card for each game for each
round of play, for batch processing on the computer. Each student receives a computer printout
for each round prior to the next set of decisions. The printout shows all factors that are
relevant to analyzing results. The students can easily relate past decisions to outcomes, and
can use that information for the next round of play. A summary sheet for use by the instructor
is printed out for each round of play.

The precise values of the demand coefficients may or may not be revealed to the students.
The instructor might reveal only a probability distribution for each coefficient, while not
revealing the precise value in the computer program, or he may give no hint of these values,
thus forcing the student to do some analyses to get estimates of them. It is less frustrating
to the student, but perhaps less realistic, when coefficients are revealed. Even when revealed,
the game retains its intrigue from term to term because the values can be changed periodically,
resulting in a new set of optimal decisions each time. Presumably, the taster the student
reacts to these changes, the better he understands the underlying economic principles.

The instructor can invent ways to make changes in these coefficients meaningful and
interesting to students. For example, in pure competition the instructor might announce that a
new contract, has been signed to ship so many units ot product to Japan as a result of removal of
tariffs, and that this has caused the demand curve to shift X number of units to the right. The
student will then be expected to react appropriately to this change in his next round of
decisions. The junior author sent notice of such events through the campus nails, with the
unexpected result of making Micromod a topic of major interest in the Campus residence halls.
The senior author has received calls well into the evening from students asking about certain
fine points. One student called at 11:30 one night to announce that he had just successfully
written and debugged a computer program that would print out the results of all possible profit
maximizing decisions in pure monopoly.

Students may be given any number of goals, including profit, return on investment in fixed
cost, market share, sales dollar, return to advertising dollar, and others. The instructor may

133

-W.

assign om? or more of goals and evaluate student performance accordingly. Students Bay bo

instructed to compete with each other, or they may be given some absolute standard tor which to

str i ve.

Empirical Study

The use of microood as one of several bases tor determining course grades provides
incentive for the students to put forth a full effort in making his decisions. Without this
incentive, experienced teachers know that the game would become a frivolous endeavor for most
students, and very little economic analysis would be used for miking decisions. Since this
incentive is essential, teachers must question whether oicromod performance is a valid basis for

grading. The criterion used to judge validity in this study is whether raicromod performance is

an indicator of achievement in economic understanding. A second question to ask is whether
performance in micromod is biased toward students with mathematics backgrounds.

Evidence relating to these two questions was obtained from analysis of data collected from

two classes ot the author at 1'rew University. A linear multiple regression equation was

estimated for each class. The results are shown below:

Winona State College:

Y = 48. lag ♦ 7. 3 9 p X •• 2. J1 8Z

Coefficient of multiple determination « .250

Drew University:

Y = 64.800 ♦ 6 . 2 b 0 X - . 440Z

Coefficient of multiple determination - .445

The variables are:

Y = An index measuring performance in the throe micromod games

X = Average grade in the principles of economics courses

7. = Average grade in college mathematics (4.00 ~ A, zero if no college math

had been taken)

The regression coefficients for X were significantly different from zero at the 5% level in
both cases, while the coefficients for Z were not significantly different from zero. The Y
variable, performance on micromod, ic a measure of profit earned over several rounds of play in
pure competition and pure monopoly, and foe oligopoly it is a measure of the quality of a
written report describing the economic anal,:‘&£ used for each decision. Oligopoly was graded
this way because, even though a student may base his decisions on sound economic analyses, he
may not obtain high profits because his outcomes depend largely on the behavior of other firms
in the industry. These measures of performance were combined ?nto a single index to obtain
variaole Y.

Two conclusions drawn from the analysis are.

1. There is a statistically significant positive relationship beteeen micromod

pertorrance and general competence in economics.

2. There is no relationship between micromod performance and mathematical background.

The first conclusion suggests that performance in micromod seems to be an indicator of
competence in economics, so it would seem appropriate to base part of the cour.se grade on
micromod performance. It may even be appropriate to dispense with the standard lectures on
market structure and cost analysis ard use micromod as a sel f-t. eaching device. This would free
the instructor to concentrate on other more sophisticated topics.

The second conclusion suggests that the student of mathematics does not have a discernible
advantage in micromod. This is important because the mathematics background of students in
intermediate microeconomics in many schools includes the full range from little or no college
training to several courses above the calculus. The non mathematics student appears to suffer
no disadvantage in micromod, thus adding to the validity of using micromod per forma nee as a
basis for grading achievement in economics.

1 0*5

i!l® ® d£X

This paper includes a description of the structure and use of micromod, a computer game
designed for the intermediate microeconomics course* Hicroiod consists of three separate gases,
based respectively on the market environment of pure coapetition, pure monopoly and oligopoly.
Grading of game outcomes is essential to provide the incentive for serious student effort in the
gaae, so instructors should ask whether micromod performance is a valid basis for grading
achieveaent in the course. An analysis of eapirical data, using linear multiple regression
techniques concluded that aicroaod performance is a valid basis for determining course grades
since it seems to be related to achievement in economic understanding, but is not related to
mathematical background.

£OOTNOIE

part of the on-going project of designing and evaluating micromod.
in this project has been obtained from the General Research Fund ot Winona State
nd from the Joint Council on Economic Education. Adolph c. tlydegger. College of
, and Paulette A. Cichon, formerly of Northern Illinois University, wrote the
programs for Plicromod. Dr. Hanlon designed the game and has used it in several
ring the past two years.

1. This paper represents

Assistance in this projec
College a
St. Teresa

computer prog

classes during the past two years.

135

. *

HE! APPROACHES TO BUSH ESS SIBULATIOIS
J aaeis D. J. Holies
St. Andrews Presbyterian College
Ltiurinboirg, North Carolina
Telephone: (919) 276-3652

Ji ®1 l£££gft£fe£g

In looking at new approaches that are being taken ii siialatioi the first illnstratioi that
coaes to n..nd is intercollegiate coipetition. After a slow start intercollegiate coapetitioa is
beginning to spread into the hinterlands rather than being the tool of a few large uni varsities.
Two of fche oldest such competitions are those ran at Hichigan State University and Baory
University. The nichigaa State gane covers extended play for a fall senester while Bnory
restricts its coipetition to six weeks. In both cases decisions are filed by nail or TIT with a
wrap-op conference at the end of play featnring awards to the top teaas.

In lorth Carolina we have gone an additional step in establishing several intrastate
competitions. Under the sponsorship of the North Carolina Edocatioaal Coapnter Service (ICBCS) a
two day gaae was run in October, 1970. Priaarily for faculty aeabers from colleges and
universities throughout lorth Carolina response was overwhelming and provided the iapetus for
the first student competition which was held in February, 1971. At the student conference there
were 27 schools represented by 3-aeaber teaas. £fce Executive Gaaef 1 1 (TRIG) by flenshaw and
Jacksos was chosen for both faculty and student conferences because of its comprehensive mature
and yet relative ease of play.

Cash prizes were awarded to the three top student teaas by a lorth Carolina baa h and an
award of a snail aaount of free CPU tiae was given by ICECS to the institution sponsoring the
top ceaa. It would be aa understatement to say that the response to this coape titios was
over whelaing. All decisions were aade on the preaises of the Triangle Universities Coaputatioa
Center over a span of two days. Exciteaeat was at a high level during the entire session and
peaked quite high at award tiae on the afternoon of the second day.

Based on the success of this first student coipetition plans are being aade at the tiae of
this writing for a continuation of the intrastate coipetition. During the spring of 1972 a
coipetition based on TEIG and played on site over two days will be held for junior and coaaunity
colleges in lorth Carolina. These institutions are quite enthusiastic over the use of
simulations but their students are at a disadvantage when competing against students froa four-
year colleges and universities. Later, daring the fall of 1972, a gaae and conference using
IITQP-Interaatlonal Operating s^aulationf 21 by Thorelli and Graves will be staged for four-year
colleges and universities. Play will extend over inch of the fall senester with decisions being
submitted through terminals tied to the Triangle Universities Conputation center. The gaae will
then culainate with a one-day conference for awarding of prizes and critique of qaae play. It
is anticipated that participation in these two coapetitions will be quite extensive and
spirited.

In adainisterlng different siaulations, it has been ay observation that aore often than aot
students sub-optiaize their decisions because repetition is not keen enough to force then to do
otherwise. In 1963 Thoaas Hcffaann of the University of Binnesota began work on the concept of
using the coaputer as a participant thus causing students to do a better job of decision-aakiag.
Using the analogy of par in golf, Hoffaana established a system of heuristic rales which gave
the coaputer player superiority aot because of greater knowledge of the aatheaatical structure
of the qaae bat rather "as a result of its inherent requirements of consistency, comprehensive
analysis, and logically derived decisions." The vehicle used for this experiaeat was the IBB
flaaageaeat Decision-Baking Laboratory, Bodel 1* . Professor Boffsana is aot presently engaged ia
research of this nature but the original gaae package has served as the basis for three recent
doctoral dissertations. [ 3]

After tbe tiae I learned of Hoffaaan’s work I had begun to braiastora with a couple of
students over the idea of letting the coaputer use regression analysis to bacons a participant.
Learning of Hoffaan's research strengthened ay belief and during the winter of 1971 I began
writing a subroutine for an existing siaulatioa which would allow the coaputer to becoae a
coapetitive participant. By hypothesis was that the coaputer can generally do a better job of
decision-making than aost students if it has the possibility of using objective aatheaatical
tools which aost students will not be using, and that students are basically coapetitive and
will do a better job when facing draaatic defeat by a Machine. In the initial part of the
project a subroutine was written to incorporate regression analysis into Tl^g Execqtive Game.
Heuristic rules were then establish* which would use the results of regression in asking
decisions.

In actual play decisions relative to price, targeting expenditure, and research and
development expenditure are developed as variants fros the aean of each of these factors for all
of the teaan. Desand is then estisated by the equation

with fc*2 1 b^, b4 being correlation coefficients relating the Independent variables of price,
marketing, cesear^L auu development, and econosic index to the dependent variable of desand,
other decis< j:is such as production schedoled, raw aaterlal purchases, and aainteoance
expenditures logically follow. Since regression analysis requires observations of historical
data the conputer buys such data with other teaas being given the sane opportunity.

The first run of this package, referred to ais TBXGCT (the Executive Gase - Conputer Teas),
was aade in the sunder of 1971. During the previons spring a senior senlnar had participated is
TEXG with eight teans for twelve periods of play. These decisions were replayed in the snnner
against the conputer teas. Such an approach left so chance for interaction or learning os the
part of the non-coapu ter teaas but did provide a valuable first test of the hypothesis. TRIG
incorporates a year-end run in he regular gase which evaluates teans on the basis of profit
earned and dividends paid assigning a rate of return to each teas. The conputer teas placed
second ou* of nine teaas with a return of 2,219%. The leading student teas showed a return of
2.234% and the third place student teas showed a return of 1*135%. The other student teaas fell
off sharply 'tlth two teans showing negative returns.

it the beginning of the fall semester, 1971, eight volunteer student teans were recruited
and an interactive coapetition began. Since the teans were nade up of volunteers there was no
worry about grades or aoy facnlty pressure. During the twelve periods of play two teans were
forced into absolute bankruptcy. A student tean placed first with a return of 3.419%. In second
place the conputer tean shoved a return of 2.226% and the third place student tean shoved a
return of 2.098%. It is necessary to jention that bias exists in these resnlts in that one
Btiuer of both the first and third place tease had participated 1q the spring play. The rate of
return for other teans fell off sharply with one tean at 1*383% and the other three below 1.0%.

During the spring of 1972 TEXGCT will be nsed as a partial reqnirenent for the senior
senlnar. It will be interesting to observe this competition wherein the students will feel the
pressure of grades, their peers, and the conputer tean, all at one tine. Hopefully, sech an
experience will give then a sanpling of pressures that exist in the business world.

Too often in business simulations » it hors and publishers have tended to overlook the
potential afforded by role-playing while emphasising the decision-naking process. Sone authors
pay lip service to the need for role-playing by including vlth their gane the request that a
president, vice-president, and secretary-traa^nrer should be decided upon early in the qane and
that the president should be responsible for having the decision forn conpletnd when the
adninistra tor cones for it. The best gane play I*ve ever adnlnlstered vas a situation in which
the decisloa-nakiug portion of the gane vas sonevhat weak bot gave the opportnnity for labor-
rjanageneet confrontations and negotiations. Vlth two hard-boiled facnlty nenbers as union
representati ss, the negotiations often becane too realistic to be enjoyable fron an
adninistrator • s point of view. After participating in that particular sinulation one student
reconnended tint I add the roles of supplier of raw materials and consnner of finished goods to
those of union and nanagenent with the supplier and consnner being external to the gane. The
student further proposed that participants vould shift fnnetions during the gnnn with each
participant getting to play each role one-fourth of the tine. Tine has not pernitted ne to
explore the proposal but I think there is considerable nerlt in such an idea.

In using sinulation as a teaching device I have been faced with the problen of grading
participants. For nany years 1 rejected every schene that I could think np after a one-time
trial. During 1970 I uoved to peer grading and vas veil satisfied after using it during one
course. The sane approacl vas also nsed doring the spring senester of 1971 and will be used
during the spring of 1972.

The sanple fora at the end of this paper shows the approach I have taken. In snnnary, each
student on a tean provides a quantitative valuation of hinself and his tean nenbers based upon
quality and quantity of contribution to tean effort, accuracy of work performed, dependability,
and initiative. Each student is then further asked to provide a prose consent on overall
perfornanco for each of his teaa nenbers* it this point I enter the grading process through
valuation of the prose consents, fly effect is snail, however, due to a weight of only one out of
a total of eleven being assigned to ny rating o'c the prose evaluation. Fpr tho total nlnnlation
I then use the following weights:

Y » a + bjXj + ^2x2 + b3x3 + b4x4

Individual Peer Hating

40%

Teaa Hank in Final Results
Based on Profit Produced

30%

flaa ariuaUtioi of Stratagy 20ft

ui Kaailta Bafort Paaal of
Jalgaa

Tana Evaluation by Iaatractor IQft

100*

luAai Umkii is£ lit atm

I do aot pro fas a to have special insight into tba probiaa srtas of siaalatioa; hovever,
tbara are several araaa that obviously aaad davalopaaat or inpeovaneat. Oaa of such probleas ia
tba general uavillingness of pabliabara to accapt any responsibility for providing iaforaatioa
otbar tbaa vbat ia faraiabad ia tba atadaat aad adaiaiatrator aaaaala. Soaa gaaas ara vail
docuaeated aa to optioaal foatnraa aad ragairaaaata for iaplaaaatatioa oa coaputer ayataaa otbar
tbaa tbe oaa for vbicb tba aiaalatioa vaa originally vrittaa. Hovever, otbar vail publicized
quaes ara vary poorly docnaaatad* In oaa inataaca I talked vitb iha "author" of a gaaa vbo aftar
a fav ainotaa of gaaationiag adaittad ba knev littla about tba prograa bat anggaatad I call Joa
saitb vbo did tba prograaaiag foar yaara ago aad vaa nov ra port ad to ba ia Hoastoa, Tonal I
faal that it ia aandatory that pabliabara acgaaint tbaaaalvaa vail aaongb vitb aiaalatioa
techniques aad docaaantatioa ragniraaanta to aatabliab ataadarla to ba aat by aay aatbor soaking
publicatioa of a gaaa*

Belative to tba actual rnaaiag of a gaaa, I faal that va aaara ara ganarally gailty of poor
adaiaistratioa. Bora enjoyaeat aad iaprovad laaraing raault froa an adaiaiatrator vbo ia aot
oaly antbnaiaatic about gaaiag bat ia vail varaad in tba dataila of tba gaaa baiag adaiaiatarad.

1 final araa vbicb aaat ba davalopad bafora aiaalatioa caa taka ita rightful placa aa a
poverful ta aching tool ia tha diaaaniaation of naar iaforaatioa an a state, regional, and
national baaia* So badly aaad to kaov what ia baiag dona ia raaaarcb loading to davalopaaat of
nov aad diffaraat aiaulatioaa. ia furthar naad to knov both objectively and aabjactivaly tba
expariancaa of aaara of publiahod gaaas* If car tain gaaas ara poorly docnaaatad aad bard ta
iapleaent, this should ba convayad to tba pabliabar and to oar callaaguaa. Obviously va aaat aaa
discration and tact vitb a purposa of producing battar aiaalatioa a ratbar than blasting a
particular pabliabar or author* It ia ay baliaf that a fraa exchange of iaforaatioa caa
troaaadoasly lacrosse tba quantity and quality of aiaulatioaa and traaandously incraaaa tba
nuobar of usara of this vary iaportaat tool.

BBFBBBBCBS

1* Benshav, Bichard C. , Or., aad Jackson, Janas B*# Tba Ixacntlve Sill* Hoaavood, Illinois*

Bichard 0* Irvin, lac*, 1966*

2. Thorelli, Baas 8. and Sravaa, Bobart L., IBTOP-In tec national Ouaca^^ous Simla tiei* Bav
York* Praa Press of Gleacoe, 1968*

3* Braascb, John, "Easiness Gaaas, Prograaaad Playar, and Individual Decisioa~Raking

Profiles," Uni varsity of flinnescta, 1966*

4* Bliasoa, ilan, "B Study of tba Bffact of Poraal Training in tba ipplication of Quantitativa
Hodala to Production as Bavaalad by aa Iataractiva Decision Siaalation," University of
Rinnaaota, 1970*

5* Scbaid, H* Gilaa, "in Bzpariaant on tba Reliability and Validity of
Heasure, Profits, ia Tvo Ranageaent Gaaes" Oaivaraity of Rianeaota, 1969.

128

139

tba Parforaaaca

COHPOTBR SI ISOLATION OP ECOHOBIC HODELS FOR INSTRUCTIONAL USAGE

Stanley iilson and Ra y Billingsley
Texas ASH University
College Station, Texas 77843
Telephone: (713) 845-5443

An acadenic discipline is a systea of concepts and hypotheses. These concepts and
hypotheses are viewed separately as abstractions fros reality and constitute, for the sost part,
the subject natter of a discipline. Host disciplines view this part of their subject natter as
theory. Other concepts consist of the relationship between these abstractions. This latter is
particularly crucial to a discipline because it contains the discipline's way of approaching
reality, i.e., its technigue of analysis. The facts of reality and thus the abstractions fron
reality change, but, presnnably, the techniques of analysis continue to be valid. They nay be
added to and inproved but hopefully not invalidated. To the extent that an individual knows
these nethodological concepts - to that extent he is a practitioner of the field. It follows
that training the student in a field consists of inparting these nethodological concepts to hin
and giving hin practice in using then.

In order to teach nethodology there nust be a transportation (i.e., connunicatioa) of these
concepts fron the intellect of the instructor to the intellect of the student. Direct
connunication of the intellect of one individual to the intellect of another is (at least in our
current state of technology) inpossible. Thus, the concepts nust be enbodied in sone physical
nediun and this nediun presented to the student's senses in the hope that he will abstract the
concept fron the nediun. It follows that the nediun nust be chosen and used with the objective
of naxinizing the ability of the student to abstract fron it. Bach particular nediun or language
has particular advantages and disadvantages. The optinun choice nay well be several nedia used
in conbination.

This analysis applies at least as well to econonics as to other disciplines. Bcononics, in
particular, nakes use of several languages in conbination to convey its concepts and techniques
of analysis. These include the written or spokea word, graphs and nathenatical fornulas. The
concepts of econonics relate various elenents in the econony in a cause-effect relationship. For
exanple, the concept "denand" relates price (the cause) with guantity purchased (the effect).
Denand nay be conveyed in words, in a nathenatical fornula or in the forn of a graph.

The basic nethodology of econonics consists of building and using econonic nodels. An
econonic nodel nay be defined as a ays ten of econonic concepts. The nodel proports to be an
abstract representation of a part or all of an econonic systen. The technique of econonic
analysis consists of four steps: (1) concepts are defined, (2) concepts are put together (or
related) to forn nodels, (3) changes are introduced in the nodels, and (4) the effects of these
changes are noted. Econonic nodels serve two purposes. First, they are a nethod by which
economists can perforn experiments. Unlike the physical scientist, social scientists cannot
experinent directly on that area of reality they are studying. Secondly, econonic nodels give
students practice in using econonic concepts (i.e., practice in perforning econonic analysis) •

A conputer nodel is a particularly effectively nediun for allowing students to introduce
changes and observe the effects. This is because a conputer nodel (or progran) is a sequence of
instructions to the conputer telling it to sinulate or act like the econoaic entity being
nodeled. If the conputer is to accurately conforn to the set of concepts in the intellect of the
econonist, then it is vital that consideration be given to how these concepts can be enbodied in
a conputer progran. To illustrate the problens of progranning econonic concepts, several
concepts and approaches to progranning then will be exanined.

flfttfc&t ggullibriun

The first and sinplest nodel presented to econonics students in the sinple aarket nodel.
This consists of three concepts: (1) denand, (2) supply, and (3) equilibriun price and

quantity. The concepts, denand and supply, are easily enbodied in a progran because they are
already in the forn of nathenatical equations.

Quantity Denanded * f (Price)
Quantity Supplied * f (Price)

129

140

These becone:

QD = *D - BD I PED

and

QS * AS - BS x PES

where the parameters for demand are AD, BD and BD and those for supply are AS* BS and BS. Other
forms of these equations nay be utilized also. Alien gives several forms of the demand curve (2,
p. 114). There exist several computer languages (including FORTH AH) into which it is easy to
translate such functional forns.

The concept of aarket equilibrium or movement toward equilibrium is another natter,
however. There is no nathenatical statement of this process. The condition of equilibrium is
easy to represent. Is is that quantity demanded equal quantity supplied (QD * QS) • But, the real
process of how equilibriun is actually reached remains a mystery, tfalrus asserted a tatannenent
or "groping** toward equilibriun but no one seems to have gone beyond this, including modern
economists. See Patinkin, for example, (10, pp. 38-43).

One can, however, deduce several characteristics which the equlibriun process must have if
it is to actually achieve or arrive at that price where QD * QS. First of all, the equilibriun
process must essentially be a process of changing the price. Second, the direction of the price
change must depend on which is larger, QD or QS. If QD x QS, the price must go up. If the
reverse is true, the price must decline. Finally, the size of the change in price must be
proportional to the size of the surplus or shortage. Letting DBLP be the change in price, the
following equation achieves these conditions.

All terns in this equation are positive so that if QS x QD, the (QD - QS) will be negative and
thus DELP will be negative (the change in price will be declining). Notice that the value of
DELP depends not on the absolute size of QD - QS (the surplus or shortage) but on the relative
size. One intuitively feels that the power of the force making for the price change depends not
on the absolute size of the surplus but on the size of the surplus relative to the total size of
the market. The size of the aarket is interpreted to be the amount bought and sold (i.e., QD and
QS). The size of the market is thus interpreted to be (QD ♦ QS)/2; i.e., the average of QD and
QS.

An effect of this formulation is that as the price approaches the equilibrium price, the
size of (QD - QS) becomes smaller, relative to (QD ♦ QS) , thus DELP becomes smaller and the
price converges on equilibrium. In this way the price doesn'.t oscillate about the equilibrium
indefinitely. KDP is the constant of proportionality. It nay be set to 1.0 for a normal market.
For a cobweb effect KDP can be made larger. The larger the value of KDP, the greater the
oscillation. Thus, the model can be made to converge on the equilibriun price or oscillate as
one wishes. Even if KDP had a value of 1.0, a cobweb effect could be achieved if one selected
functional forns and/or parameter values which produced the appropriate elasticities of deiand
and supply.

A program (called HARKET) has been written, utilizing the formula discussed above, and has
been used to teach the introductory principles course. It seems to have been successful in
demonstrating the equilibriun process. Bach student chooses a set of parameters for the demand
and supply functions as well as an initial price. The initial price is used to calculate QD and
QS.. These are then printed out along with the price. The program then calculates DELP and adds
it to P. Then it uses this value to recalculate QD and QS and print then out along with the new
price. The last few lines of printout show no appreciable difference in QD and QS and thus no
appreciable difference in price. This demonstrates to the student the concept of equilibriun.
That is, if the price is not at equilibriun, it will converge on equilibrium and when it reaches
equilibrium, it will remain there. This demonstration is particularly effective because the
student gets to select parameter values and the initial price. This demonstrates that the
system will seek equilibriun for a wide variety of initial conditions.

There is no inplication that the equation given above "explains** how the aarket reaches
equilibriun. But the equation does make the model perform like economists envision that the
market performs. If the price is to converge on equilibrium, then the changes in price nust be
smaller as price gets closer to equilibriun. One way to achieve this is to make the change in
price proportionate to the difference between the price and the equilibrium price. This could be
done by solving for the equilibriun price but it would imply that the market "knew** the
equilibriun price. The function outlined above assumes only that the price change is influenced
by the relative size of the surplus or shortage.

QD - QS

DELP

x KDP

(QD + QS) / 2

130

Shifts in Denand and Supply

MARKET also allows the student to introduce changes in denand and/or supply. This is
acconplished by introducing changes in the paraneters of the functions. The nodel first seeks
the equilibriun price and then# once this is achieved# the change in the

Thus (QD2 - QS2) >0,0 thus (QD1 - QS^^) <0.0

and DELP > 0.0 and DELP < 0.0

Quantity

therefore P will increase

therefore P will decline

function parameter is introduced. If the change is in the denand function# then# at the
equilibriun price achieved# quantity denanded is no longer what it was. Thus# QD - QS f 0.0 and
the prograa prints QD# QS# and prioe# changes price again and seeks the new equilibriun. If the
change is in a supply function paraneter# a sinilar process ensues. In this way# the student can
introduce changes in the nodel and observe the effect on the nodel.

The different paraneters have different effects on the functions. AD and AS change the
price intercept of their functions and shift then in a parallel nanner. 0D and BS change the
slope or angle of their functions. ED and ES change the curvature of their functions. Together#
these six paraneters give the student the ability to change the denand and supply in any
conceivable nanner.

A second progran# SIMPLE FIBB # sinulates a firn with cost and revenue function. It nakes
use of sone of the concepts described for BASKET. The firn's average revenue function is:

AR = A - B X QE

where AB is average revenue# Q is the quantity of output and A# B and E are paraneters. The
narginal revenue is the first derivative of total revenue. Average variable cost is:

AVC = XQ2 - XQ2* 2.

Marginal cost is the first derivative of total cost. The student specified a beginning quantity
of output as well as the paraneters for the cost and revenue functions. If HC / MB# then the
quantity is changed by DELQ. The fornula for DELQ is:

DELQ

KR - MC

x CDQ.

(MR + MC) x o.5

The above foraula has the sale fora as that for DELP in NARKBT and for analogical reasons.
The function coapels DELQ to converge on the profit aaziaizing level of output (when NC = NR) by
saaller and saaller aaounts. This iaplies that if the firs is at an output level where NB z NC ,
it will ezpand output and that the change in output will be proportionate to the difference
between NC and NR. A siailar iaplication holds when NR z NC. The prograa also calculates total
revenue, total cost and profit. This is particularly useful because the student can observe that
profit increases as the prograa aoves closer to the quantity where NC = NB. One useful approach
is to rerun the prograa with the saae set of paraaeters but with the initial output level being
on the other side of the profit aaziaizing level of output froa the first initial output level.
Por ezaaple, if the profit aaziaizing level of output was 120 units and the first initial output
level was 150 units, it is useful to rerun the prograa with an initial output level of about 90
units. In this way the student sees that profit increases as the output level approaches 120
units no natter fron which direction and thus that profit is nazinized where NC > hb. This has
proved to be a useful way to reinforce this inportant, and by no aeans easy to grasp, concept.
Indeed, SINPLE FIBH has proved to be substantially superior to written or graphic denonstrations
and ezpiantions of this concept.

A third prograa, FACTOR-PRODUCT, siauiates a firn*s econoaic responses associated with a
production function of the fora

Y = f(X).

The prograa lists the paraneter values for the production function and the prices assuaed for
factor, I and product, ¥• Starting with a beginning value for X, the prograa calculates and
prints all of the relevant econoaic variables for each iteration as the calcuations aove toward
equilibriua. These include: (1) the quantity of X, QX; (2) the price of X, PX; (J) total fized
cost, TPC; (4) the quantity of Y, QY; {5) the price of Y, PY; (6) total revenue product, THP ;
(7) the net revenue, NB: (8) the aarginal physical product, NP; (9) the value of the aarginal
product, VHP; (10) the average product, AP;(11) the average revenue product, ARP; (12) the
aarginal cost, NC and finally (13) the stage of production the calculation refers to. These
stages are indicated as 1, for increasing returns to scale, 2, for dininishing returns to scale
and 3, for decreasing returns. An option available on the data cards allows the prograa to run
past the point of econoaic optiuun so that all stages of production can be illustrated if the
production function used allows for all stages. In its present fora, four types of production
functions are included in the prograa. These are:

(1) Cobb-Douglass

Y = Z x xB

(2) Quadratic

Y = A + (B x x) - (C x X2)

(3) Quadratic Root

Y = A + (B x X°-5) - (C x x)

(4) Cubic

Y = A + (B x x) + (C x X2) - (D x x3).

FACTOR— PRODUCT searches for that level of usage of the resource X, such that profit is
aazinized. This position is achieved when two conditions are net. They are (1) PX = VHP (in the
case of pure coapetition) or NC 3 VHP and (2) VHP is declining. This is a particularly
interesting condition because with many production functions a VHP curve will be generated such
that PX = VHP at two positions. When FACTOR-PBODUCT locates such a position, it checks to see if
VHP is declining about that position as X increases. If it is not, it continues to search by
increasing X. This is an ezaaple of eabodying econoaic principles into a coaputer prograa.

FACTOB-PRODUCT, like all of the other siaulations, aust have soae rule for deciding how
auch to change X. The foraula is similar to the ones used before.

MC - VMP

DELX = x CDQ

(MC + VMP) / 2

The output denonstrates
profit rises to a peak.

to the student that as X gets closer to the level where VHP = NC, the

143

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132

A Hacrogcono|ic Bod el

An-other model written and utilized was a simulation of a sinple Keynesian nacroecononic
nodel. This program, called KEYNES, besides having a consumption function also has a marginal
efficiency of capital function and an interest rate determined by a money market. The money
market is of particular interest bebause it has a liguidity trap. See Ackley (1, pp. 192-194,
384-385).

The user specifies a beginning income level and interest rate as well as parameters for the
consumption function, NEC curve, liguidity demand for money curve and transaction demand for
money, taxes and government expenditures. The program calculates the consumption and investment
levels and sums then along with government expenditures to get total expenditures. Investment
is determined by the interest rate through the 8 EC curve. The interest rate chosen is the
equilibrium interest rate which is determined by the money market. The money market functions in
a similar manner to the process described for HA 2 SET above. The only exceptions are that the
supply of money is perfectly inelastic (and given by the user) and that below a certain interest
rate (specified by the user as an option) the demand for money is perfectly elastic.

Once total expenditures are calculated and the other values calculated, they are printed
out. Then the program sets income in the next iteration egual to total expenditures, and the
values are recalculated. This continues until equilibrium is reached (where total expenditures
egual income). The path toward eguilibrium is not necessarily a straight one. The changes in
income not only change consumption but also the transactions demand for money. This shifts the
total demand for money, thus changing the eguilibrium interest rate and investment. Thus, a
convergence toward eguilibrium may follow a cyclical path.

Once the model reaches eguilibrum, it introduces any changes the user specified in function
parameters or amount of taxes or government expenditures. Then it does the calculation again and
begins a movement to the new eguilibrium position. The movement toward equilibrium income does
not require the calculation of a change in income such as MARKET requires the calculation of a
change in price. The new income level is determined by the previous expenditure level. The rule
that expenditures in one period equal income in the next period automatically assures a movement
toward eguilibrium income. This feature assists in conveying that important principle of
macroeconomics. Unlike MARKET and SIMPLE FIRM, KEYNES is not suitable for an introductory
course, but is suitable for an intermediate macroeconomics course. Like the other two models,
KEYNES has been used in economics classes.

Classroom Usage and Testing

No matter how well a computer model simulates a part of the economy, if it is to be a
useful teaching technigue, it must be integrated into the course. That is, the model must be an
integral part of lectures, discussions, outside class activities and testing.

To do this one begins by emphasizing in his lectures that economic concepts and models can
be communicated in several languages, that each language has its advantages and disadvantages
and that computer codes are one medium or language in which economic models can be expressed.
The course becomes a seguence of models. The lecturer begins each model by defining the concepts
in several different languages (words, graphs and equations) • Then he puts the concepts together
to form models in these various media, introduces changes in the models and observes effects.
This gives a general outline to the lectures, i.e., the series of lectures on each model can be
divided into the four steps referred to earlier, with computer output used as an exhibit when
one comes to the lectures on introducing changes and observing effects.

Students can be assigned the task of selecting a set of original model parameters and one
or more changes in parameters. These can then be run using the program deck and the results
used by students as the basis of classroom discussion or as an extra example to be used, along
with their notes and the text, for studying. A second subject of discussion is the flowchart.
The instructor can treat the flowchart as another language or medium of expressing the model.
Alternately, one can suggest that the class attempt to flowchart the model during one class
period. This exercise is particularly useful for bringing out any weaknesses in the students1
understanding of the model. Those who have programmed know that unless one knows the process or
system precisely one cannot program it. Attempts to program, particularly at the flowchart
stage, bring out any hidden defects in ones understanding. A person may believe he understands
something until he attempts to explain it to a computer. The student can participate, at least
vicariously, in this discovery of ambiguity by participating in the flowcharting process. Works
on flowcharting are available. See, for example, Chapin [5] and Farina [8].

Computer models can also be used as part of lab sessions or as individual work. To make
programs available and useful there are two requirements. First, the computer code must be
available to the student. The code may be in the form of a card deck, or the program may be on
the system. In either case, the emphasis must be on convenience of usage. The second requirement

133

is the availability of a good (i.e,, clear and conplete) documentation for each model used.
There are standards of documentation which are available[ 4 ], Bach of the prograns mentioned has
been docunented (with the exception of FACTOR-PRODUCT and its documentation is now being worked
on) and references to these can be found in the bibliography.

It is unfortunate, but true, that most students are oriented toward tests. If something is
covered in class but mill not be on the exam, they give it only passing notice; allocating their
tine to those things they will be tested on. Thus, if computer models are to be used
effectively in a course, they must somehow be on the examinations. One way this was done was to
have a takehone exam in which the questions consisted of a computer printout. The examination
process consisted of the following:

1* Bach student chose numerical parameters for the model and also chose changes,

2, These were run on the computer and the printout for each student’s parameters
were given to him,

3* The student took the printout home and used it as the basis of his
"examination, "

4, He was graded on how well he explained the model and how well he explained what
the model was doing (what his printout said).

It should be observed that the students were not only having a takehone exam, they were
also, in effect, writing their own exam questions. If a student caused his model to perform a
number of complicated, interesting changes, then he had a number of complicated, interesting
changes to explain, his work was of a higher quality because of the nature of the questions, and
thus he got a better grade. Those who performed simple experiments had a less sophisticated
explanation and thus received an average grade. There were also, of course, those who failed or
received a ’D1,

This approach to lectures and examinations was tried out at Texas Southern University, The
general effect seemed to be that students’ grades improved by about one letter. That is, those
who had been making C’s now were making B’s, However, not all students improved. It is difficult
to determine whether the improvement was due exclusively to the use of computer models or
whether the takehone exams afforded then the opportunity to express themselves better because
they were not under tension. It is obvious, however, that the performance of the class was not
lowered, and this was at the sane time that they were receiving a more rigorous introduction to
economics, an introduction to the use of computers and an introduction to computer modeling of
economic systems.

REFE8EHCES

1* Ackley, Gardner, Macroeconomic Theory, Hew York: Hacnillian Company, 1961,

2* Allen, ft, G. D, , Mathematical Economics, London: Hacnillian Company, Ltd,, 1965,

3, Bilas, Bichard A., Microeconomic Theory: A Graphic Analysis, Hew York: McGraw-Hill, 1967.

4, Billingsley, R, and Stanley Wilson, Program and Model DocumentationStandards. Program

and Model Documentation 71-1, Department of Agricultural Economics, Texas A6H University,
February 1971,

5, Chapin, Hed, Flowcharts. Hew York: Auerbach Publishers, 1971,

6, Farina, Maria 7,, Flowcharting. Englewood Cliffs, Mew Jersey: Prentice-Hall, 1970.

7, Ferguson, C. E, , and Charles Maurice, Economic Analysis. Hew Tork: Bichard D. Irwin, Inc.,
1970,

8, Haylor, Thomas,? Joseph Balintfy, Donald Burdick, and Kong Chu, Computer Simulation
Techniques. Hew Tork: John Wiley and Sons, Inc,, 1966,

9, Orcutt, Guy H, , "simulation of Economic Systems," Americas Economic Review 59 (Dec, 1960).

893-907, -

10, Patinkin, Don, Money. Interest apd Prices, Hew Tork: Harper and Row, 1956,

11, Sanuelsoa, p. a.. Found at tom of Econgpiy Analysis. Cambridge: Harvard University Press,
1948,

134

145

12* Veintraub, Sidney, price Theory lev York: Pitaan Publishing Corporation, 1949.

13. lilde, D. J«, Qptiaqa Seeking Methods, lev Jersey: Prer tice-Hall, 1964.

14. Hilson, Stanley E«, Eqonoiic Model - Market* C'* router Prograa Docunentation for Texas

Regional Acadeaic Coaputer Expedient, Departaent of Industrial Engineering, Texas A6N

University, Copes Pora lo. 13*

15. iilson, Stanley B., Econoaic Ho del - Simple Fin* Coaputer Prograa Docunentation for Texas

i Regional Acadeaic Coaputer Expedient, Departaent of Industrial Engineering, Texas A6N

University, Copes Fora lo. 14.

16. Iilson, Stanley E., and Stedaan Cary, Keyses-Coinuter Simulation of a Hacroeconoaic Bodel.
Coaputer Prograa Docuaentatioa for Texas Begional kcadeaic Coaputer Bxperinent, Departaent
of Industrial Engineering, Texas kSH University, Copes Fora No. 10.

135

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136

Problem: Contiuous line design/non-maze pattern

COBPUTER ASSISTED INSTRUCTION IM ECONOMICS
AT THE UNIVERSITY OF KOT8E DABE

Prank J. Bonello and William I. Davisson
University of Notre Dane
Notre Dane, Indiana 46556
Telephone: (219) 283-6335

Introduct ion

The development of the computer represents one of the major technological changes of the
last twenty years. Although colleges have had access to these machines since the very beginning
of their development, only recently have attempts been Bade to utilize computers as learning
tools. Indeed up until the last few years only selected students, namely physical science and
engineering students, came into direct contact with the computer. The object of this contact was
primarily to give the student an ability to utilize the services of a high speed calculating
machine or electronic slide rule. Recently however, attempts have been made to broaden student
use of the computer so that business, social science, and humanities majors are also exposed to
the computer. Bore importantly attempts have been made to enlarge the role played by the
computer within the educational prooess, to make it a viable learning tool[ 1 ].

These developments owe their origin to several different technical and educational advances
including: an increase in faculty knowledge and appreciation of the computer, the development of
simple computer languages, and the development and extension of interactive or tiie sharing
systems. These last two elements represent major forces leading to change. The development of
simple computer languages has reduced significantly the time which both students and faculty
need to expend in order to acquire an ability to communicate with the computer. The development
and extension of time sharing and remote terminal facilities has reduced wait time for answers
almost to zero; indeed in some cases instantaneous two way communication between the computer
and the faculty or student user is now possible. This of course has created many new
possibilities for the use of the computer as an educational tool.

Within the context of the social sciences, a computer cat function as a demonstration
facility, as an automatic corrector with built in teaching assistance, and as a "real world"
environment tor the testing of alternative hypotheses. At most colleges there has been some
implementation of computer assisted instruction (CAI) in each of these three areas.
Unfortunately, this has generally occurred only in piecemeal fashion. To fully exploit the
potential of CAI, it is necessary to establish a fully integrated system, a system that employs
the computer in each of the three noted functional areas, in the Economics Department at the
University of Notre Dame we are using such a system. The purpose of this paper is to give a
report on our progress to date. Bore specifically we discuss each of the functional areas,
indicate what we feel are pedagogical advantages and disadvantages, and provide examples drawn
from elementary and intermediate level macro and micro economic courses.

The Computer as a Deaonstra t ion Pacil it y

Frequently in Economics it is useful to demonstrate or underscore theoretical properties or
conclusions by means of numerical examples. For instance in macroeconomics certain models are
presented which have the property that a dollar*s increase in government expenditure has more
of an expansive impact on national income than a dollar*s decrease in taxes, A teacher having
presented such a model, indicated the particular property, and established the conceptual basis
for such a conclusion might seek to reinforce this conclusion by a series of numerical examples.
To do so during class time might involve too heavy a time cost and to assign the examples as
homework involves the same heavy time cost and a tedium that both students and teacher wish to
avoid. If however, the student has access tc a computer terminal and is able to call a routine
that will make the necessary calculations, the series of examples can be processed in less time
than would be required to complete a single example manually. The instructor must provide the
necessary input data. The student uses the computer to make calculations. The calculations are
made and the answer given in such a way as to demonstrate a particular property.

In order to utilize a computer effectively in this way several prerequisites must be
satisfied. First, the teacher must present the argument conceptually. In terms of the above
example the instructor must not only present the appropriate model but also argue or explain the
conceptual basis for the particular conclusion. Secondly, the instructor must assign problems
and input data which obviously employ the same basic model and which numerically highlight the
particular conclusion. Third, the computer routine utilized by the student must employ the same
basic model and yield output in a form which underscores the particular conclusion.

The advantage of using a computer as a demonstration facility t*. that a large number of
nuserical examples aay be processed in a very short period of time. Rot only can a particular
conclusion be demonstrated but the reasons shy a particular result obtains can also be
illustrated. This is accomplished by having the student knowingly switch models. Thus all
changes within a model can be explored and compared with all changes within some other model.
Tine no longer imposes itself as a constraint and the tedium involved in making similar
numerical computations is removed. There might even be some gain in student enthusiasm if
students are, as sometimes rumored, enamored with conputers[ 2 ]• Finally all this is possible
without the student being required to learn any computer programming whatsoever: gnestions
concerning numerical inputs are asked by the computer and the student simply supplies the
numbers.

There are several disadvantages although some can be avoided if proper caution is
exercised. First, both the student and the instructor nay become too problem or number oriented
and, consequently, too little emphasis is given to understanding the theory which underlies the
numerical results. Secondly, a full range of routines nay be desirable and the instructor, at
least in the beginning of CAI, must devote some tine to the programming of demonstration
routines and the preparation of appropriate numerical examples.

Having set the stage for this first use of the computer let us present examples from both
microeconomics and nacro<*cononics.

Case 1: Microeconomics

The first micro calculating routine that we use at Notre Dane is called HU (Micro-
Instruction 1) . Sample output from nil is illustrated in Figure 1. The program is written in
BAS IC[ 3 ).

The program begins by printing out the available options, or what it can do. The student
selects an option; as in Figure 1 supply elasticity. In certain instances the student must
select a particular model within the option by specifying what independent variables are
included within the model. The model is presented, input is requested, and the answer is given.
The student is then given the choice of changing an input within the given model, switching to
one of the other available options of terminating the session.

This program with its various options allow* several demonstrations, with the quantity
demanded option the inverse relationship between price and quantity demand is easily indicated
and demand schedules or Engel curves can be readily constructed. Effects of income changes as
well as the effects of changes in the prices of complement and substitute commodities on
quantity demanded can also be easily indicated. The quantity supplied option seeks to indicate
the direct price-quantity relationship for supply. The various elasticity options simply attempt
to facilitate computations. The student can also use the various options in conjunction with one
another: use t'e quantity demanded option to generate a demand schedule (or Engel Curves) and
then the demand elasticity (or income elasticity) option to calcuate the demand elasticity
coefficient over various range of the schedule and thereby verify that the demand elasticity
coefficient is not necessarily a constant over the entiro demand schedule.

Case 2: Macroeconomics

MAI (Macro Assistance 1) represents our first macroeconomic calculating routine. Sample
output is illustrated in Figure 2 and the program is also written in BASIC.

The program begins by printing out five alternative macro models, identified as nil through
MA5. The student selects a particular model and provides the input requested. The values of the
endogenous variables are then calculated and printed. The student then has the choice of
modifying a variable within that model, switching to a different model, or terminating the
session.

The student by using this program can fully explore the implications of changing the
exogenous variables within a model. Then he can switch to another model and fully explore that
model. He then can compare differences in results for the two models; that is, isolate the
effects in terns of modified numerical results of similar exogenous variable changes between the
two models.

Thg Computei; a§ a Teaching Assistant

There has been a continuous advancement in the role played by the computer and optical
scanning equipment in the grading of objective exani nations[ 4 ]. But the computer can do even
more within this particular education context. It can be programmed to ask questions or set up

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problems which the student aust solve in a Banner that becones progressively no re advanced, lm
such routines the coaputer can inaediately tell the student whether he is right or wrong and if
he is wrong the coaputer can supply additional infornation or ash additional questions which
will indicate to the student why his initial response was incorrect. In this way the coapnter
acts as a real teaching assistant and not nerely as a test corrector.

If a series of objective questions are used , the student sinply calls out the routine while
sitting at the coaputer terninal. The coaputer prints out the initial question which the student
answers. If the answer is correct the coaputer proceeds to the next question. If the answer is
incorrect the coaputer noves into a subroutine which asks the student further questions or
provides further infornation so that the student can understand why his initial response was
incorrect and why the correct answer is whit it is.

To achieve naxinun effectiveness using this approach, the student probably should cover
certain assigned naterials before using these prograns. In this way the student is tested on
what he knows in a review situation, floreover, there should be relatively close coordination
between test routine material, course content, and actual test naterial. Only if this is the
case will the student perceive soae positive benefit fron the use of the test routines.

The advantages of the objective question routine are very nuch the sane as the advantages
of any test except the student is in no way penalised for poor performance and there is
immediate instruction on any incorrectly answered question. The disadvantages are that the
student night becoao too machine- oriented and indeed light rely too heavily on the test
routines as a Beans of achieving satisfactory grades. A further disadvantage is that a great
deal of time is neressary to construct this type of routine especially when the objective
question takes th<j fora of a nultiple choice question. This night involve an instruction
subroutine for each incot :ect foil.

If problems are used rather than ''Mective questions soae new considerations eaerge but he
operational elements reaain auch the sape„ The student calls out the appropriate routine which
contains the problems. If f student gives a correct answer te the Initial problea another and
more difficult problea is presented, if an incorrect response is given the coaputer asks the
student additional questions or provides further infornation so that the student can understand
why his initial response was incorrect and why the corract answer is what it is.

The problea approach has several advantages, first it is quite amenable to a policy format
which students seen to find interesting. Again using the context of an intermediate
macroeconomic theory course, aodels are employed which allow for both monetary and fiscal
policy. Thus the student night be given a problea based on such a nodel where he is ashed to
manipulate policy in order to achieve a given goal; say, nake aggregate deaand equal to
aggregate supply. The student then attenpts to sake the necessary policy adjustment. A second
advantage of the problea approach is that it nay reduce the tine required for the preparation of
test or review routines.

Perhaps it is advisable to sake several connents regarding the advantages of the computer
in this pretest or review context vis-a-vis problea sets or workbooks. The computer approach is
much more flexible. First numerical problems can be processed aore quickly electronically.
Secondly the computer routines allow for instant instruction - the follow-up questions or
information which lead the student to the correct answer if he nakes a mistake. Thirdly because
a different environment is used and if care is taken in the construction of the routine, the
review can be less tedious. And again there is no requirement that the student acquire any
proqraaming knowledge whatever.

Case 1: Microeconomics

MI4 is a general objective question routine. Sample output froa BI4 is illustrated in
Figure 3. The program is written in BASIC.

The progtau is a ~eview of supplv and deaand and focuses on the factors which affect
demand, the facte rs which affect supply, and the effects of changes in deaand and supply. The

routine includes several aultiple choice questions and soae true or false and yes or no

questions. In each instance there a student gives an incorrect answer, he is given infornation
which will help hin get the correct answer and the question is repeated. The student cannot

select particular questions but aust proceed through the entire ten question routine. The

information provided at the very beginning of the prograa is a review and is considered
sufficient for the correct answering of all the questions.

The dialog froa programs )1I6 and H 1 7 shown in Figures 4 and 5 represent a sonewhat
different use of the "tutorial11 program approach.

EDIT MIA BASIC
EDIT RUN

THIS PROGRAM IS A MICRO REVIEW ROUTINE.

YOU ARE GIVEN A MARKET MODEL AND TESTED
TO DETERMINE WHETHER OR NOT YOU CAN
MANIPULATE CERTAIN VARIABLES IN THE MODEL IN
ORDER TO ACHIEVE GIVEN OBJECTIVES.

THE DEMAND EQUATION I St
Qla<A-<B*P>'t<C*Y>-<D*Pl>+E*P2)>/P
WHERE

A-CONSTANT TERM

B-COEFFICIENT WHICH REPRESENTS THE WAY IN WHICH
Q1 CHANGES WHEN OWN PRICE CHANGES
P-OWN PRICE

^COEFFICIENT WHICH EXPRESSES THE WAY IN WHICH
Q1 CHANGES WHEN Y CHANGES
Y-INCOME

D-COEFFICIENT WHICH EXPRESSES THE WAY IN WHICH
Q» CHANGES WHEN THE PRICE OF COMPLIMENTS CHANGE
PI -PRICE OF COMPLIMENT

E-COEFFICIENT WHICH EXPRESSES THE WAY Q1

CHANGES WHEN THE PRICE OF SUBSTITUTES CHANGE
P2-PRICE OF SUBSTITUTES

THE SUPPLY EQUATI ON I St
Q2-(F ♦ CG*P>-(H*P1 >>/P
WHERE

02-QUANTITY SUPPLIED/

F-CONSTANT TERM

G-COEFFICIENT WHICH EXPRESSES THE WAY 02 CHANGES
WHEN OWN PRICE CHANGES/

P-OWN PRICE/

H-COEFFICIENT WHICH EXPRESSES THE WAY 02 CHANGES
WHEN PRICE OF INPUTS CHANGE/

PI -THE PRICE OF INPUTS.

THE FIRST QUESTION ISt
IF YOU WISH TO INCREASE MARKET PRICE AND
QUANTITY/ WHAT WOULD YOU DO?

ANSWER ’INCREASE DEMAND* /' DECREASE DEMAND'/
'INCREASE SUPPLY'/ OR* DECREASE SUPPLY*

"INCREASE DEMAND"

YOUR ANSWER IS CORRECT

THE SECOND QUESTION ISt
IF INCOME INCREASES WHAT HAPPENS TO DEMAND?

ANSWER ’INCREASES' OR 'DECREASES'.

? "DECREASES"

YOUR ANSWER IS INCORRECT. THE RELATIONSHIP
BETWEEN INCOME AND DEMAND IS DIRECT.

THE SECOND QUESTION ISt
IF INCOME INCREASES WHAT HAPPENS TO DEMAND?

ANSWER • INCREASES' OR 'DECREASES' .

FIGURE 3.

,*52

MI6

EDIT IBJ|T MI6 BASIC

THIS PROGRAM EXAMINES THE BASIC IDEAS OF A PRODUCTION FUNCTION*
DIMINISHING RETURNS AND THE STAGES OF PRODUCTION.

DO YOU WISH TO HAVE THESE TERMS DEFINED?

ANSWER "YES" OR "NO" .

? "YES"

A PRODUCTION FUNCTION IS A TECHNICAL RELATIONSHIP THAT
INDICATES THE AMOUNT OF OUTPUT THAT CAN PHYSICALLY
BE PRODUCED BY EACH FACTOR OF PRODUCTION OR BY EACH
SET OF FACTORS OF PRODUCTION — I .E.* LAND* LABOR* CAPITAL
OR MANAGERIAL ABILITY.

A PRODUCTION FUNCTION IS ALWAYS DEFINED FOR A GIVEN
STATE OF TECHNOLOGY. THE USUAL FACTOR THAT ESTABLISHES
THE STATE OF TECHNOLOGY IS THE CAPITAL OR PLANT AND
EQUIPMENT. ONCE THE INVESTMENT IS MADE IN EQUIPMENT IT
IS FINANCIALLY PROHIBITIVE TO INVEST IN NEWER EQUIPMENT
UNTIL THAT GIVEN PLANT AND EQUIPMENT IS PAID FOR.

DIMINISHING RETURNS MEANS THAT AN INCREASE IN
THE VARIABLE FACTORS OF PRODUCTION (AS INPUTS) WILL INCREASE
OUTPUT. HOWEVER, AFTER SOME POINT IN PRODUCTION THE
INCREASE IN OUTPUT FROM EACH SUCCESSIVE EQUAL INCREASE IN
THE VARIABLE INPUT WILL BE LESS AND LESS BECAUSE OF THE
FIXED FACTORS.

ECONOMIES OF SCALE ASSUMES A GIVEN STATE OF TECHNOLOGY
AND REFERS TO THE RELATIONSHIP OF INPUT CHANGES TO
CHANGES IN OUTPUT.

ASSUME A GIVEN PERCENTAGE CHANGE IN ALL INPUTS.

IF OUTPUT CHANGES BY THE SAME PERCENT WE REFER TO
CONSTANT RETURNS TO SCALE. IF OUTPUT CHANUES BY A

SMALLER AMOUNT OR PERCENT WE REFER TO DECREASING RETURNS TO SCALE
IF OUTPUT CHANGES BY A LARGER AMOUNT* INCREASING
RETURNS TO SCALE WILL OCCUR.

DO YOU WISH THE PRODUCTION FUNCTION TO BE DEFINED?

ANSWER "YES" OR "NO" .

? "YES"

A GENERAL PRODUCTION FUNCTION MAY BE EXPRESSED:

OUTPUT IS A FUNCTION OF LAND INPUTS* LABOR INPUTS* CAPITAL I NPUTS* ENTREP
RENEURIAL INPUTS AND A TECHNOLOGY FACTOR. EACH
ITEM CAN BE REPRESENTED BY A SYMBOL:

RESPECTIVELY LAND = L* LABOR = N * CAP I TAL = C* AND
ENTREPRENEUR = E AND TECHNOLOGY = T.

THUS OUTPUT = T(L*N*C*E)

TO MOVE FROM A GENERAL TO A SPECIFIC PRODUCTION FUNCTION
DETAIL MUST BE ADDED TO INDICATE THE EXACT NATURE
OF THE RELATIONSHIP BETWEEN OUTPUT AND THE INPUTS.

A PRODUCTION FUNCTION MIGHT BE AS FOLLOWS:

OUTPUT = T(N*C>

OUTPUT = T ( N*K ) WHERE K IS THE FIXED INPUT SET.
what IS THE INITIAL INPUT LEVEL OF N (LABOR)

? 200

A NUMBER BETWEEN 1 AND 5 WILL INDICATE A LOW LEVEL
OF TECHNOLOGY* BETWEEN 60 - 100* A HIGH LEVEL.

WHAT IS THE VALUE OF THE TECHNOLOGICAL FACTOR?

? 5

FIGURE H.

153

142

| 106

1 OUTPUT - TCN/K) WHERE K IS THE FIXED INPUT SET.

I WHAT IS THE INITIAL INPUT LEVEL OF N (LABOR)

? 200

' A NUMBER BETWEEN 1 AND 5 WILL INDICATE A LOW LEVEL

OF TECHNOLOGY. BETWEEN 60 - 100. A HIGH LEVEL.

WHAT IS THE VALUE OF THE TECHNOLOGICAL FACTOR?

? 60

k A NUMBER BETWEEN .1 AND .5 WILL INDICATE A

AUTOMATED OR HIGH FIXED FACTOR FIRM. A NUMBER BETWEEN
1.0 AND 2.0 WILL INDICATE A SEMI -AUTOMATED FIRM OR

A tOW FIXED

FACTOR FIRM.

? #3

LEVEL

TOTAL

VARIABLE

TOTAL

AVERAGE

MARGINAL

PRODUCTION

INPUT

OUTPUT

PRODUCT

200

80000.

400.00

220

176000.

800.00

4800.00

240

432000.

1800.00

12800.01

260

831999.

3200.00

20000.18

280

1399997.

5000.00

28400.23

300

2939992.

9800.00

77000.69

320

3135990.

9800.00

9800.02

340

3331988.

9800.00

9800.02

360

3527985.

9800.00

9799.97

380

3532884.

9297.10

244.95

400

3533006.

8832.55

6.10

420

3533009.

8411.97

0.15

440

3533009*

8029.61

0.00

WHAT IS THE TOTAL FIXED COST OF THE PLANT. OR FIXED COSTOF THE FACTORS.
? 1S0000

WHAT IS THE COST OF HIRING EACH VARIABLE INPUT FOR THE PERIOD?

? SOO

FIGURE 4. Continued.

« ;* , )

ERIC

143

154

LEVEL

TOTAL

PRODUCTION

OUTPUT

80000.

176000.

432000.

831999.

1399997.

2939992.

3135990.

3331988.

3527985.

3532884.

1 1

3533006.

3533009.

LEVEL

AVERAGE

TOTAL

PRODUCTION

COST

3.125

1 .477

0.625

0.337

0.207

0. 102

0.099

0.096

0.094

0.096

1 1

0.099

0.102

MI6

TOTAL

VARI ABLE

FIXED

COST

100000.

150000.

110000.

150000.

120000.

150000.

130000.

150000.

140000.

150000.

160000.

150000.

1 69999.

150000.

179999.

150000.

189999.

150000.

199999.

150000.

209999.

150000.

219999.

150000.

AVERAGE

VARIABLE

FIXED

COST

1.250

1.875

0.625

0.852

0.278

0.347

0. 156

0. 180

0. 100

0. 107

0.051

0.048

0.051

0.045

0.051

0.043

0.054

0.042

0.057

0.042

0.059

0.042

DO YOU WISH TO CHANGE SOMETHING?
ANSWER "INPUT” OR "COST" •

7 "NO"

EDIT

FIGURE 4. Continued.

144

TOTAL

COST

250000.

260000.

270000.

280000.

290000.

300000.

310000.

319999.

329999.

339999.

349999.

359999.

369999.

MARGINAL

COST

1.250

0.104

0.039

0.025

0.018

0.006

0.051

2.041

81.966

3333.292

Program BI6 constructs and defines a particular production function. It then develops the
physical product schedules {Total Product, APPV and HPP) • Next, fixed and variable cost input
allows the development of the total and per unit cost schedules.

Progran HI7 is a set of IS questions, shown in Figure 4, keyed on the output fron HI6. If
the student gives an incorrect answer, he is provided additional information and the question is
asked again. This demonstration is keyed to the intermediate microeconomic book by R. Leftwich.

Case 2: Hacroecononics

Our most elementary nacro policy routine is called GH15. Figure 6 is sample output. The
program is also written in BASIC.

In this case it is presumed that the instructor has provided an explanation of the
underlying nacro model. If the student makes an incorrect policy decision he is simply told that
he is incorrect. Further information or explanation is not provided because the only ingredients
necessary for a correct decision, the difference between "GRP* and 'Full Employment GRP* and the
value of the " mult ipl ier, " are printed out once the student supplies the initially reguested
input.

The dialog fron progran HA 3 is shown in Figure 7. It is designed to illustrate the IS and
LR analysis. It is useful when used with the graphic IS and LN analysis.

The Computer as a "Real World" Environment f Qf the Testing of Alternative Hypotheses

In many disciplines the major objectives of instruction are to equip students with tools of
analysis and to develop within the student an ability to apply these tools in examining and
solving problems. When the computer functions as a "'real world' environment for the testing of
alternative hypotheses," it is providing the student an opportunity to apply tools in examining
and solving problems. Such routines have certain basic characteristics, primarily in terns of
format. First the routine provides the student with basic data— the initial state of the world.
Secondly the student acting as a decision maker must manipulate certain variables in order to
achieve specific goals. This manipulation of variables is based on student's theoretical
knowledge as reinforced or supplemented by his examination of the basic data. Thirdly a new set
of data emerges which embodies the results of the student's initial manipulation of variables.
At this stage the student can ascertain the results of his decision and his success as a
decision maker. The routine can provide for further decisions with further data output or It can
terminate the program after only a single set of decisions.

There are of course many differences between such routines. One difference is in terms of
the number of decision makers: the individual versus the group game. In the group game each of
several students or several groups of students manipulates or makes decisions for a single firm
or a single country. The second set of data which emerges contains the results of all these
different decisions. Thus the student is competing against other students and must in some cases
anticipate their decisions. In such instances batch processing is required. If only a single
individual is involved there is no simultaneous interaction of decisions so that the second set
of data simply reflects the decisions of the single student. In this case tine sharing can be
used.

Another difference is in terns of* the types of changes which occur between stages. In the
simpler versions the only source of change is the decision of the student as caused by a change
in a policy variable. In more complex versions there is systematic variation in non-policy
exogenous variables as well. Indeed the student is usually required to recognize such changes if
he is to make correct policy decisions. Finally there are versions in which a third type of
change, random change, is added. This is usually included for the sake of realism; that is, the
future is not perfectly predictable and consequently even the most carefully designed policy can
be frustrated by random change.

These routines also vary in other respects including the number of goals to be achieved,
the number of policy &riables over which the student has control, and the compa tability of
goals. Some routines even include statistical sub-routines that the student can use in examining
and estimating behavioral relationships within the "real world" of the routine.

To fully exploit the intellectual potential of this role of the computer is extremely
difficult. First the routine must be constructed so that the student cannot achieve success by
luck but at the sane time allow for experimentation which will lead to understanding. Secondly,
the real world contained within the routine must bear some similarity that basic behavioral
patterns are iaaediately obvious. Thirdly, if statistical procedures must be used to estimate
the magnitude of certain relationships, the student should have some basic understanding of
these procedures.

HUN

THIS TUTORIAL PROGRAM IS DESIGNED TO BE USED WITH
PROGRAM MI 6 ON PRODUCTION AND COST FUNCTIONS.

DO YOU WISH THE DEFINITIONS AND INSTRUCTIONS FOR THIS PROGRAM?
ANSWER* "YES" OR "NO".

? "YES"

THE TERM * LEVEL OF PRODUCTION* IS USED IN THIS PROGRAM
TO REFER TO THE TABLE OUTPUT COLUMNS OBTAINED FROM MI 6.

YOU WILL NEED THE OUTPUT FROM MI6 IN WORKING THIS PROGRAM.

YOU WILL ALSO NEED THE BOOK, * PRICE SYSTEM AND
RESOURCE ALLOCATION* BY R. LEFTWICH.

WHEN AN ANSWER IS REQUIRED THAT RELATES TO THE LEVEL OF PRODUCTION
YOU MUST BE CAREFUL TO PROVIDE ONLY A SINGLE PRODUCTION
LEVEL, OR A BEGINNING AND ENDING PRODUCTION
LEVEL AS REQUIRED BY EACH QUESTION.

QUESTION It

DOES "DIMINISHING RETURNS TO SCALE" MEAN THE
SAME THING AS "DIMINISHING TOTAL PRODUCT INCREASES"?

ANSWER! "YES" OR "NO".

? "YES"

YOUR ANSWER IS CORRECT.

QUESTION 2:

IS THE LAW OF DIMINISHING RETURNS MEASURED ON THE
AVERAGE OR MARGINAL PRODUCT SCHEDULE?

ANSWER * AVERAGE* OR • MARGINAL* •

? "AVERAGE"

YOUR ANSWER IS INCORRECT. SEE LEFTWICH PP. 117, 119.

QUEST I ON 2t

IS THE LAW OF DIMINISHING RETURNS MEASURED ON THE
AVERAGE OR MARGINAL PRODUCT SCHEDULE?

ANSWER ’AVERAGE* OR 'MARGINAL*.

? 'MARGINAL"

YOUR ANSWER IS CORRECT.

QUESTION 3t

WHAT LEVELS OF PRODUCTION INDICATE INCREASING RETURNS TO SCALE?
? 2,7

YOUR ANSWER IS INCORRECT. RECHECK THE SCHEDULE.

SEE LEFTWICH, P.119, FIGURE 7-1.

QUESTION 3 t

WHAT LEVELS OF PRODUCTION INDICATE INCREASING RETURNS TO SCALE?

? 1,6

FIGURE 5.

157

146

EDIT CL(GNl) BASIC
EDIT RUN

THIS IS A SIMPLE MULTIPLIER MODEL STUDY OF EMPLOYMENT THEORY.

WHEN THE PROGRAM ASKS FOR INPUT THAT

IS IN THE FORM OF A NUMBER* INCLUDE THE DECIMAL POINT AND
THE APPROPRIATE SIGN AS REGUI RED FOR EACH INPUT SITUATION.

WHEN ALPHABETIC INPUT IS REQUIRED BE SURE TO ENCLOSE
THE INPUT IN QUOTATION MARKS

WHAT IS AUTONOMOUS CONSUMPTION
7 IOO

WHAT IS THE PROPENSITY TO CONSUME OUT OF GNP
7 .78

WHAT IS GOVERNMENT DEMAND FOR GOODS AND SERVICES
7 ISO

WHAT IS INVESTMENT DEMAND
? 175

THE MULTIPLIER IS A. 545453

GNP IS 1931.817

FULL EMPLOYMENT GNP IS 1738

TO REACH FULL EMPLOYMENT* BY HOW MUCH SHOULD GOVERNMENT DEMAND CHANGE
? -43

YOU ARE CORRECT

WOULD YOUR LIKE TO CHANGE SOMETHING?

ANSWER "YES" OR ••NO".

? "YES"

AUT CON* MPC* I* OR G
? "MPC”

WHAT IS THE NEW VALUE FOR MPC
? »8S

THE MULTIPLIER IS 6.66666S

GNP IS 2546.666

FULL EMPLOYMENT GNP IS 2724

TO REACH FULL EMPLOYMENT* BY HOW MUCH SHOULD GOVERNMENT DEMAND CHANGE
? 30

YOUR ANSWER IS WRONG! THAT WOULD CAUSE GNP TO BE 2746.666
TO REACH FULL EMPLOYMENT* b’ HOW MUCH SHOULD GOVERNMENT DEMAND CHANGE
? 29

YOUR ANSWER IS WRONG! THAT WOULD CAUSE GNP TO BE 2739.999
TO. REACH FULL EMPLOYMENT* BY HOW MUCH SHOULD GOVERNMENT DEMAND CHANGE
? 28

YOUR ANSWER IS WRONG!THAT WOULD CAUSE GNP TO BE 2733.333
TO REACH FULL EMPLOYMENT* BY HOW MUCH SHOULD GOVERNMENT DEMAND CHANGE
? 27

YOU ARE CORRECT

WOULD YOUR LIKE TO CHANGE SOMETHING?

ANSWER "YES" OR "NO".

? "NO"

EDIT

FIGURE 6.

... 158

14?

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ise

The advantages of such routines lie primarily in the experience which the student obtains
in attempting to solve problems on the basis of his knowledge and ability. The demand to make
material relevant is frequently a demand to use knowledge in solving current real problems. Thus
by the use of the computer in this way not only does the student gain experience in an area in
which experience is obtained only with difficulty if at all, but at the very sane tile
demonstrates for himself the necessity and usefulness of theoretical knowled ge[ 6 ].

The major disadvantages reside primarily in setting up the routine so as to achieve maximum
intellectual gain. If a number of stuv'.ents are making decisions simultaneously and batch
processing is required, the instantaneous communication between student and computer is
eliminated. If there is no interaction of student decisions then some realism is lost. At Notre
Dame we have both types of programs.

CASE 1; Microeconomics

A case where microeconomics can effectively simulate a real world situation is in a market
type relationship where the student must act as if he were a part of an overall business
environment. AGSIM[7] is such a program. It is a general simulation that involves two elements:
(1) a specified macro economic model and (2) students acting as competitive business firms
within a competitive market in an attempt to earn a profit.

The output from AGSIM is presented in Figure 8. The program is written in PORTRAN. In this
program the instructor established the macro model, he sets variables like the average
propensity to consume, the federal tax rate, government purchases per firm, and government
transfers per firm- The price of the good is also set by the instructor. Each student acting as
a firm makes his own decisions in each period regarding sales and investment. The results are
calculated in the context of both the specified macro model and the competitive market which is
represented by the interaction of decisions by all students. The student gets computer output
tor each successive period. He must examine tbis output before making decisions for the next
period. The teacher may periodically change the macro environment or he may modify the
'•com pet it i ve market price."

CASE 2: Macroeconomics

Price stablility and full employment are explicit goals of the American economy. With GM6
we have attempted to create a situation where the student can manipulate both monetary and
fiscal policy in order to achieve both of these goals. One problem is that the two goals are not
fully consistent with one another; zero price change and zero unemployment are not
simultaneously possible. Another aspect of realism is a continuous growth in the productive
capability of the economy.

Figure 9 represents output for program Gn6. we can follow the program as it operates for
the stu dent [ 8 ]. The program asks if instructions are desired, and if they are, the information
is printed out. Next the program asks if the student desires to see the model, which is printed
out ii desired. Then the student puts in each of the four variables as shown, ten quarters for
each variable. To control the variables, he simply changes the magnitude of each variable in
successive quarters- The answers are printed out as shown in tbe last half oc Figure 9. After
each set of output the student may branch back to change any variable, or he may end the
program. The program is written in BASIC. The instructor usually sets the policy goals for the
student, i.e., GNP, full employment GNP, unemployment 6%, price change -6 per quarter, etc.

Conclusion

This represents then the status of our attempt to develop a complete system of CAI within
Economics. Our objectives over the immediate future are to fill in gaps in terms of available
programs and to obtain more experience with the system within the classroom setting. Once this
is accomplished we can begin to test whether or not CAI is an effective educational tool.

Even though we are only at the initial stage of CAI ve feel that aside from current
resource limitations, the use of the computer as an instructional device is limited only by our
own imaginations. Hopefully this paper by pointing out and exploring alternative educational
roles for computers will stimulate and encourage further investigation and experimentation with
CAI.

1 49’

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t'.' 15162

CH6

EDIT CL( GM O BASIC
EDIT RUN

DO YOU WISH INSTRUCTIONS ON HOW TO RUN THE PRO GRAM 7
ANSWER •YES' OR 'NO*

7 "YES"

DATA MUST BE ENTERED BY VARIABLE. THE FIRST DATA IS
THE AMOUNT OF PERSONAL TAXES. THE SECOND IS THE
AMOUNT OF CORPORATE TAXES. FOLLOWED BY THE MONEY
SUPPLY AND THE AMOUNT OF GOVERNMENT EXPENDITURES.
DATA ARE ENTERED IN A ROW FOR THE TEN QUARTERS.
CORPORATE TAXES OF AS BILLION WOULD BE ENTERED AS AS
DO YOU WISH TO SEE THE MODEL?

ANSWER ’YES’ OR 'NO*

7 "YES"

DEFINITIONS AND RELATIONS

(3NP = CON ♦ INV + GOV

CON = C + MPC+DI

DI = GNP - CPROF - PTAX

CPROF = H+GNP

INV =11+ A+RE + G+RATE

RE = CPROF - PTAX

RATE = U+MONEY + V*GN P + 16.0

POTENTIAL OUTPUT COMPUTED FROM A COBB-DOUGLAS
PRODUCTION FUNCTION.

GNPF = TECH* A * LAB* B * CAP*C WHERE A+B+C“l
ENTER DATA FOR PERSONAL TAXES C 10 QTRS.)

? 90.90.90.90.90.90.90. 90. 95. 95

ENTER DATA FOR CORPORATE TAXES ( 10 QTRS. >

? A5.A5. A5. A5. AS. A5. AA.A3.A2.A2

ENTER THE MONEY SUPPLY (10 QTRS)

7 200.200.200. 200. 200. 200. 200. 200. 200. 200

ENTER DATA FOR GOVERNMENT EXPENDITURES (10 QTRS.)

7 2 1 5. 2 1 5. 2 1 5. 2 1 5. 2 1 5. 2 1 5. 220. 220. 220. 220

QUART

EDIT

FIGURE 9.

-•>.* I

,163

016

QUARTER

GNP

POTENTIAL GNP

DISPOSABLE INCOME

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959.0

587.6

752.9

968.9

58 7.6

752.9

978.8

587.6

752.9

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1038* 1

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1048.0

597.4

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INTEREST RATE

PRICE CHANGE

UNEMPLOYMENT

7.904

3.447

8.947

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3.688

9. 188

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CO YOU WISH TO CHANGE A VARIABLE? ANSWER THE VARIABLE NAME IN QUOTES OR
•NO ' .

THE VARI ARLES ARE "PRIVATE TAXES" "CORPORATE TAXES"
"MONEY SUPPLY" AND "GOVERNMENT EXPENDITURES"

? "NO"

EDIT

FIGURE 9. Continued.

ERIC

153

FOOTNOTES

1. For alternative examples of the use of computers in undergraduate prograns see Proceeding*

pf a Con f era nee on Computers in the Undergraduate Curr icula (Iowa City: Center for

Conferences and Institutes, University of~lowa, 1910) and Second Conference on Computers in
the Undergraduate Curricula (Hanover: University Press of New En<?lacd7 1971) • For

additional examples within Economics see New Developments in the f^achinq of Economics
edited by K. G. Lunsden (Englewood Cliffs: Prentice-Hall, 1967) and Recent Research in
Economic Education edited by K. G. Lunsden (Englewood Cliffs: Prentice-Hall, 1970). See
also Davisson, tf • Information Processing: Applications jp the Social and Behavioral

Sc ‘ ences (New York: Appleton Century Crofts, 1970)*

2. See Sharac, J. and D. Russ, "Evaluation cf Student Learning and Inforaation Utilixation in
a Computer Simulated Economic Model" in Second Conference, pp. 94-9U.

3. BASIC is a time-sharing computer language.

4. Kel 7, A. C. "The Economics of Teaching: The Role of Tips" in Recent Research, pp. 44-66.

5* Modified from a BASIC Drogram obtained from George Pilot, Department of Economics,

Dartmouth College.

6. Perhapi another advantage is that such routines are on the market. Two examples are:

Econometric Gaming: A iiiA for Computer Analysis by L. R. Klein and H. K. Evans (New York:

The Macmillan Company, 1969) and fia^ra: A Game of Growth and Policy by Peter Lindert (New

York: Holt, Rinehart and Winston, 1970). ~

7. Modified from a FORTRAN program supplied by Professor Bonney, Luther College, Iowa.

3. Modified from a FORTRAN program supplied by Professor Bonney, Luther College, Iowa.

1£5

154

INTEGBATI MG COMPUTER PROGRAMS IN ECONOMICS VIA TIME SHARING TERMINALS

Prank DePelice
Belmont Abbey College
6elnont, North Carolina 28012
Telephone: (704) 825-3711

lAUadacUaa

Siialations of the various functional areas of business based on conplez interactive nodels
are used alnost routinely at large universities, and hardly at all at snail liberal arts
colleges. The universities have their ovn large computers and computer personnel vhereas the
typical snail liberal arts college nay have a terminal in a tine-sharing systen and a part-tine
faculty nenber as terninal nanager. Given these differences in hardware and back-up personnel,
it is easy to see why snail colleges are not aaking nuch use of the conplez interactive business
sinulations. However, it is technically feasible, and not really very difficult, to run these
sinulations o vor low speed tina-sharing terminals if two conditions are net.

First, the faculty nenber nust be notivated. He nust go to the aountain, the
nountan will not cone to bin.

Second, there nust be good people at the heln of the tine-sharing systen to help work
out the inevitable problens of adapting prograns for use over a terninal.

A nuch easier way of using conputer prograns in economics is to use canned prograns that
are available fron the program library of the tine-sharing systen. When using this type of
progran, the najor problem is not technical adaptation as with the large simulation prograns but
proper integration within a specific course. And as before, the use of this type of progran,
reguires faculty motivation and it assunes good people at the computer; otherwise, usable
prograns would not be available to the terminals.

In North Carolina we have the necessary good people running a state-wide time-sharing
system: North Carolina Educational Computing Service (NCECS). There are over 50 colleges served
by the IBM 370/165 at the Triangle Universities* Conputer Center (TUCC), which is in Durham and
owned by Duke, UNC, and N. C. state. I was notivated to see what could be done with the conputer
fron terninals in economics. Thus, the two necessary conditions to nake the technically feasible
a reality were net. What I did was to integrate the conputer in various ways in every course
that I teach in economics.

The second part of this paper details the specific prograns and courses in ny experience
and focuses on the pedagogical problens of fitting conputer prograns into traditional courses.

The third section deals with technical problens, both with hardware and software, and their
solution. Sone tentative conclusions based on ny several years ezperience using conputer
programs as a teaching tool and some optimistic plans X have for future uses of the conputer
will oe aired in the fourth and final section of the paper.

I nake no apologies for the fact I use "someone else*s" prograns, i.e.,‘I did not write any
of the prograns I use nyself. We have cone to the point in the road, in ay opinion, at least in
the area of business and economics, where proliferation of prograns often reveals a very
inefficient duplication of effort. With good documentation properly disseninated, tine and money
can be used nuch more efficiently by adapting ezisting prograns than by writing new ones. Effort
can then be concentrated on the problens of imp lenentation and the development of new teaching
units employing the computer. It is the purpose of this paper to shed sone light on the problens
encountered in these two areas.

Ped^g ogica 1 Problems and Preparations

A computer progran can not be simply added to or inserted into nost courses without the
pre-planning sinilar to that necessary when audio-visaal supplements such as films are
incorporated in a course. First, the instructor mast have a firm grasp of the substantive natter
of the particular progran he intends to employ. He nust be certain that it is relevant to and
demonstrative of the principles and concepts he is teaching in the course. Sone of the simpler
sinulations that purport to give students a realistic learning ezperience actually teach
theoretically incorrect approaches because over-sinplif ication leaves out sone of the variables
necessary to reach correct decisions. This is the case in sone of the simple genecal business
and econonics sinulations in wide use. This is not to say that such sinple sinulations are not
useful additions to sone courses. For the typical freshman- level introduction to business
course, they serve well to give undecided majors a taste of what a business career entails and
insight into the kind of knowledge necessary for success in business. Sone of these sinple

general business simulations lave options that allow significant increases in complexity making
them much more realistic and appropriate for certain advanced undergraduate courses. On the
other hand, some simulations are so complex that they can only be used for advanced graduate
courses. Reality, of course, is quite complex, so that the more reality the instructor requires
in a simulation the more complexity in the computer simulation he must be willing to accept.
There is, then, a decision that any instructor contemplating inclusion of a simulation in a
course must make whereby he trades off some reality in the simulation for some reduction in the
complexity in the computer program and in the amount of capability necessary for his students to
gain some advantage from the simulation.

In corporate finance and several other business and economics areas, it may be a better
approach to use a complex realistic simulation almost exclusively as a second course in the
subject following the first course in the principles, concepts and theoretical tools required to
handle the problems posed by the simulation. (Many students have suggested this to me.) This
follows from the fact that simulations in finance (and other business areas and economics
generally) are primarily decision-making exercises that require the solution of certain
problems. If the instructor decides that he wants to use a simulation within a single course on
the subject, which is often a necessity, particularly at small liberal arts institutions where
there is little chance of adding a second course, he must alter the traditional course outline
in order to cover those topics where some grasp (not necessarily mastery) by the students must
precede the introduction of the simulation in the course.

A major advantage of a simulation of financial management is that it requires students to
deal with the whole range of financial problems right from their first encounter. This is far
superior to the traditional case approach where students first learn concepts relevant to one
small part of the total problei and then are asked to apply the concepts to a selected problem.
Of course, the simulation approach means that students must have an exposure to the full range
of concepts prior to any application. But the differences between the limited static case-method
and the comprehensive dynamic simulation are worth spending more tine developing theoretical
material before any application of principles is attempted. I've found that I can not get the
students to the point where they have a firm grasp of all the tools necessary before the point
in the semester when it becomes necessary to start the simulation if there is to be enough usage
of it to make set-up tine and student effort worthwhile. This means that students are forced to
jump in the water before they can really swim. Students take this as a challenge and very few
"drown." There is a need for a book in finance (which I have written and classroom tested and is
now in review) that can be used in conjunction with adequate library holdings of basic texts so
students can quickly develop the necessary analytical techniques. And pushing them into the
dec ison- making required in the simulation dramatically demonstrates to them the need to know
techniques. Also, the common student criticism that a course is just sterile theory, because
they can't see the applications, is obviated.

In the simulations I use, three or four students are assigned to each firm. The decisions
are made either as a group or they may divide them up as they see fit. Each firm is to organize
itself anyway it wants. Thus, students learn something about group dynamics and organization
automatically as a by-product. Each firm is held accountable as a group for the firm's success
or lack thereof; and a management report is required at the end of the simulation, both orally
before the class and in writing, from each firm. The simulations count for 20-30% of the
students' grade for the course, which is necessary to g uarantee conscientious effort. If the
simulation is not an interactive model, as some are not, students cannot alibi poor performance
by citing factors beyond their control. Each firm's results are a function of only its
decisions. In interactive simulations, the competitive factor is an important determinant of a
firm's performance, but students rarely cite competitors' actions as reasons for their
shortcomings.

I use two or three class sessions to explain the parameters, the variables and inter-
relationships in the simulations. Occasionally I require the students to make a set of
decisions in class. You get a better fix on who is doing what in these sessions.

After the first decisions have been submitted and run and the students have their results
back, I go over their printouts with each firm privately. Sometimes I do this during the regular
class time. I also tell them which firms are doing well and which are not. If I have just
brought thi?m their output, they are busy analyzing while I talk with individual firms. (It's
better to have the students go to the computer center to get their output, because they then see
the hardware and may develop some lasting interest in computers.) Other times I set up
conferences with individual firms during office hours. The point is that when the simulations
begin I cut down on lectures and begin to serve as a consultant. I get a copy of each firm's
output and must keep up. If I didn't they would know it in a minute when they came for help.

Giving the firms names that are the students names is a nice touch that helps motivation.
When John Jones sees the heading on his computer printout "Student, Student, and John Jones,
Inc." it helps. Each student gets his own copy of his firm's printout, which is also good as
students like to be seen on campus with a bunch of computer printout in hand.

This type of coaputer prograa which I've used in corporate finance and marketing teaches
the students nothing about computers or prograaaing but it is not intended to. Soaetiaes I
give one lecture on coaputers and prograaaing and the particular hardware set-up I'a using just
to enhance aotivation. But the coaputer prograa in this situation is merely a teaching aid.
Other prograas I use in other courses use the coaputer not only as a teaching tool but also to
teach terainal operation and prograaaing.

For exaaple, in the first principles of econoaics course (nacro) , the students are reguired
to use a canned XY plot routina that fits a least-squares line to their data. For data I have
then use the tine series of 26 aacro variables listed in the cover of their textbook. The
possible conbinations of 28 variables taken two at a tine is over 350 so that no two students
are allowed to plot the sane two variables. They nust punch up about six cards, depending on how
nany sets of data they use, connect the terninal with the coaputer, and read in their prograas.
In this case they are learning how to use the keypunch, the console-typewriter terainal, and the
card reader. Not too nuch econoaics is learned, but since the variables plotted are the national
incone accounts data this work could be inserted in the course where national incone accounting
is discussed. Better students used the opportunity to test soae elenentary theoretical
propositions, e. g. the validity of a straight line consuaption function and the Phillip's curve.
Students who conpleted the coaputer assignnent (and this was all but 5 in a class of 90) were
given a "C" for just turning in the prograa and the output. To enhance the econoaics-learning
aspect, I gave a ■B" or an "A" for a written analysis of the output. The coaputer work
constituted 10% of the students* grade.

None of the students had any background in coaputers or prograaaing. I gave one lecture on
coaputers and prograaaing in general and on the particular hardware they would use. They were
given three sheets of instructions, which I took another class period to go over. One was
instructions on how to use the key punch; one told how to use the terainal; and the third
explained, with an exaaple, the prograa they were to use. There were very few probleas at the
terainal* My student assistant put in two hours each evening for ten days at the terainal, but
probleas were ainiaal.

In ay intermediate aicro theory course I use two conversational prograas. The first is a
teaching unit on dininishing narginal utility and it fits in right after the classical
explanation for the downward sloping demand curve. Students are given an incone and soae
consuoer choices. Through choices they describe their own utility functions. The object then is
to naxinize total utility. The prograa contains four questions at the end which serve as a
write-up. The other is a cobweb aodel of supply and demand and it is used right after the long-
run equilibrium in perfect conpetition has been developed. I count the coaputer work as 10% of
the grade here also, but I require a higher quality analysis of the output for a NBN or "A”
grade.

In interaediate aacro theory I use a coaputer problea kit that contains an already punched
program of a basic aodel. It's in FOBTBA9 and the booklet has a chapter on FORTRAN to help the
students learn soae prograaaing in order to develop the nodr»l. Preparation of the students for
this computer work consists of a review of principles for which 1 require a programmed paperback
book.

Soae of the students in the intermediate level courses have had prior computer experience,
but those who have not seen to do just as well. Thirty percent of the grade is based on the
computer work in the aacro course.

Techo jca j. Trials and Tribulations

It is essential that any instructor planning to use a simulation know enough about the
technical details of the prograa to be able to communicate with the computer center personnel.
This is very iaportant in getting any program to run. Computer center personnel do not know, nor
should they be expected to know, the substantive natter and technical details of all prograas
they are asked to run. Too nany potential coaputer users know too little about coaputers - about
what they can and cannot do and generally about bow they operate. There is, then, the
possibility of a rather large communications gap between potential users of the computer and
computer center personnel. I suggest that the best way to obviate this problea is for the
potential user to learn soae programming. General introductory sessions by computer center
personnel, progranaed self-study courses in prograaaing, and regular undergraduate classes in
prograaaing, are all ways of closing the communications gap and overcoaing the general
psychological barriers inhibiting coaputer use. It is not necessary to actually become a
progranaer. The coaaon faculty consent that prograaaing is just a low level technical skill not
worthy of their tine or effort implied by "if I need it. I'll hire a prograamet*5 does have sose
validity. However, the study of prograaaing for the potential user of the computer is about like
the study of accounting for the potential businessman. He nay never actually do it hiaself but
it gives bin the ability to coanunicate with those who do; it establishes a coaaon language; and
it leads to general insights that further close the otherwise wide communications gap. The onus

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168

is OD the faculty member to Bate the first move. Closing the cobbud icatioi • s gap is the aost
important step in overcoming the inevitable technical probleas with any program.

Five years ago I brought ay first prograa to the coaputer center which had a newly
installed IBfl 360/20 with 16K core storage. As the operating systen toot up 6K, the renaining
10K was not sufficient to handle the siaulation. I was presented with two alternatives: (1)
convert the prograa froa cards to punched tape and put the prograa on over a tine-shared
teletype they had boohed up to the 360/75 at TUCC, (2) send the prograa to TUCC for then to put
on the systen, call in the input by phooe and get the output bach by nail. I chose the latter,
and by duplicating and seniing TOCC a nuaber of column coded input (decision) sheets, the
arrangenent worhed tolerably well except for the few tines when the nail was slow. What was
scheduled for classes in the course becane subject to sudden adjustnent when the output did not
cone bach when expected. Also, the students were not always able to have enough tine between
decisions if we were going to get in a sufficient nuaber of decision- nahing periods during the
senester.

Later, the core of the 360/20 on canpus was increased to 32K and it was possible to run it
there. I also used the sane coaputer when I taught the course at a nearby college. But since
that tine I have used terminals for aost of the prograns I use. One exception is whet I taught
narketing in the evenings at a junior college, largely because they have a aediua-speed terainal
in the N.C.E. C.S. system (an X BH 2780) that I wanted to try but they preferred to segaent the
program and run it on a 1620 they have that's not too busy.

The first problen encountered in modifying the sinulsttion prograa for an IBB 1050 terainal
was the slowness of the card reader; the deck is over 800 cards. I got around this by reading in
the deck over a 2780 located at another local college, also tine sharing at TOCC. Another
problea encountered is the fact the 1050 terninals I used did not have punched card output
capability and the simulations called for punched card output. I tried to modify the prograa lor
successive runs. I was not able to do this, so I modified the prograa to have the punched card
output printed and sent back on the 1050 printer with the output. At Computer Center student
assistants would then convert this back to punched cards for insertion with the input for
successive runs. However, the printout of what would have been punched cards was not colunn
coded and it took too nuch tine to get it punched in the right fields. I tried to work-up a
prograa (drun control card) for the keypunch to facilitate this punching, but the keypunches £
had to work with did not have left zero capability. The keypunch at the local college with the
2780 was used for this punching as it did have this feature. This arrangement is only practical
when just a few firas are in the siaulation for a few runs. With a nornal class of 30 and eight
runs, literally thousands of cards have to be punched. I looked into modification of the 1050
terminal to allow punched card output and found that it can be done for a nominal sub but the
NCECS operating system did not allow punched card output to be sent to 1050 terninals. (They
intended to include this capability in the system soon.) So I now run these prograas over a 2770
terainal at another college, in the systen that does have punched card output Capability-
Upgrading to the 2770 is not desirable in ay case because it cannot be operated in the CPS node,
again because of NCECS operating systea, (They intend to change this also) and the operating
costs of a 2770 terainal are not competitive with stand-alone aini-coapi ters nor with IBfl
1130's. Soae other makes of terminals are being investigated by KCECS that will provide the
necessary capabilities cheaper. With modifications in the operating system aost of the technical
problems will be solved.

Conclusions

There is a progression in teaching techniques in this general subject natter area, at the
top of which stands computer simulations. The oldest and poorest approach is the institutional,
which is purely description of the institutions in any way involved or related to the particular
aspect of business or economics being studied. Next cones the textbook with soae end-of-the-
chapter problems that give students a chance to try out basic theoretical concepts developed in
the text. Then there is the coabination text-and-casebook approach, with varying amounts of text
and with varying length cases. Sometimes the text is long and the cases short. In that situation
the case is overly simple; the student sees right through it; and itfs unrealistic. Vhen the
text is short and the cases long, the student has insufficient background in concepts to do nuch
with the case. Soae books have even gone all the way and eliminated the text completely, thereby
leaving the student to develop general principles as he struggles to solve the cases.

The computer siaulation sits at the apogee of teaching approaches because (1) it is not a
pieceneal approach like aost taxts, i.e., it combines all elements into* a reasonable whole
before the student is asked to cope with problems. This, of course, makes it sonewhat nore
difficult for the student because he is not applying a single concept to a simple problem. Be
must decide what principles apply where, and this itself is a big lesson. (2) A simulation is a
dynamic representation of reality. Textbook cases, no matter how complex and realistic, are
static; but the output from one run of a simulation becomes important input data for the next

'•v i:

158 169

ran. If students sake aistakes they must, jost as in the real world, live with then. The
conputer simulation represents a living dynamic case and a superior teaching environment*

The generally high level of motivation stimulated by using conputer programs in economics
is perhaps the most significant aspect of using them* There are a few other problems and
advantages of using computer programs in economics not mentioned above, but the advantages
outweigh, by so much, the problems, that I have planned the entire economics curriculum vith at
least one program in each course*

In addition to the six courses mentioned above, I plan to use a macroeconomic policy game
vith 10 identical countries in the international trade course* For money and banking, a
simulation of the effects of policy decisions on money supply, investment, taxes, etc* to
minimize both unemployment and changes in the price level is planned*

fly experience leads me to conclude that large scale computerized simulations are no longer
the exclusive province of universities vith large stand-alone computers* They can be used at
small schools vith lov-speed terminals* And, of course, smaller simulations and canned programs
are handled easily via terminal* I vould suggest that the minimum hardvare configuration include
punched card output capability, but everything mentioned in this paper except the programs
calling for punched card output can be run over a teletype in a time sharing system if the
instructor is motivated and the system has the kind of people ve are fortunate to have at NCECS*

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159

WOMAN by George Riske

Problem: Continuous line design/non-maze pattern

CETERIS PARIBOS METHODOLOGY AND COMPUTERIZED

~econ5mics-business models

Richard A* Stanford
Purman University
Greenville, South Carolina 29613
Telephone: (803) 246-3550

Although there are available on the market a wide variety of coaputer prograas for use in
economics and business coursesf and the developaent and use of many sore unpublished prograas
have been reported to groups of coaputer users, the application of the coaputer to econoaics and
business classrooms is yet in its infancy. Me still have hardly learned to control the coaputer,
ouch less to exploit fully the teaching capacity of this amazing result of man's ingenuity.

The range of programs published or otherwise in use is extremely broad and divert.
Professor Robert S. Holbrook, in a paper presented at the 1970 Conference on Computers in the
Undergraduate Curricula, put the problea in the following terms:

...The possible ringe is very wide, froa a simple model not unlike the blackboard
version already described in the theoretical portion of the course, to one of several
full scale econometric aodels of the U. s. economy already actually used for
forecasting and policy purposes.

I believe that both the very simple and the very complex aodels have serious
deficiencies with respect to their use in a policy game context, and that a model
between the extremes is most desirable. The simplest model, by its very nature, must
omit most of the interesting and important probleas that distinguish the real world
from the simple classroom model... Pull scale forecasting and policy models, by
definition, incorporate real world complexity, but the enormous number of inter-
relationships makes it difficult or impossible even for the instructor to trace the
paths of causation from policy to goal[ 1 ).

Professor Holbrook's objections to the very simple and the highly complex models are well taken.
I shill offer three additional critical observations about the variety of prograas which I have
seen or heard discussed:

1. Most of the programs designed for use in economics classrooms are, by model design and

program input and output formats, isolated entities with little relation to other available
programs. If the instructor wishes to use the computer to elaborate a variety of economic
mechanisms, he is confronted with a bewildering array of different program languages,

different program input and output formats, and designs for different types of coaputer
equipment. This situation is confusing to both instructor and student, especially if they
have only limited background in computer science.

2. Although some of the available programs are so simple and trivial that they accomplish

little more than do the usual blackboard expositions, most of the business oriented game
programs purport to cover as many of the routine' aspects of the f irm • s operation as
possible. The designers of economics and business game aodels often have pursued the maxim:

the closer to the "real world," the better the model. The outcome of this sort of model-
building behavior has been the appearance on the market of nuaerous hyper-coaplex game

models.

3. While there are of course available models of complexity between the extremes, nearly all
of tne game models which I have seen, whether business or economics, micro or macro, seen
to have a discomforting lack of flexibility for starting simply and progressing in
complexity.

I have nixed feelings about the use of computer models for classroom teaching purposes. On
the one hand, I am greatly impressed with what I think is tremendous teaching potential inherent
in the concept of student-participation computerized models. On the other hand, while the
available simple programs accomplish little more than blackboard expositions and lead the
students into a false sense of security in understanding relationships, the more complex
programs which I have seen seei to have the effect of frustrating the student, rather than
instructing him[ 2 ). While the complexity is more lifelike, or "closer to the real world," the
frustration resulting from the complexity seems far to outweigh the instruction which the
student receives.

These results are particularly disconcerting to an economist who has been brought Up on a
steady diet o t ceteris paribus methodology for analyzing real-world economic (including
business) phenomena. Since the economist has little access to the controlled laboratory
conditions of the natural scientist, he must in some other way abstract from the complexity of
the real world if he is to understand and teach others abr>ut the operation of economic

161

172

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ous variable
astient of
is the defl
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Id complexity, the
characteristics of a
e model, he nay draw
e conclusions may
have been adjusted s
s. The ceteris par
data to approxiaat
ation of aoney value
e period of study.

economist aay then proceed to
real-world mechanism as he
tentative conclusions aboi»t the
be tested using correlation-
tatistically to approximate the
lbus statistical methodology,
e the assumed constancy of the
time series data by a price

his students about the operation of the real-world mechanism by teaching the operation of the
model, and relating aodel conclusions (implicitly or explicitly) ceteris paribus assumptions.

All of this is very well for
or his classroom. But I think that we have
models for classroom use to implement
teacning device. Either we dwell upon the
fail to relate them to the real world,
hyper- com plex models. An example is provid
courses. If the complex business game
either the economises ceteris paribus net
operation of business or economics mechan
point of the economises procedure.

the economist in his office,
failed in large measure whe
satisfactorily our ceteris
methodology by constructing n
or we completely avoid using
ed by the game models usually
models reaching the market
hodology is considered to be
isms, or the program writers

his professional journal,
n constructing computer
paribus methodology as a
ear trivial models, but
it when we construct the
used in business policy
give any evidence at all,
useless in teaching the
have too often missed the

Section II

Professor Holbrook, in the same paper quoted above, expresses an opinion and makes a
recommendation for alleviating many of the objections expressed above:

The best model for game use is one which is sufficiently complex to include important
dynamic characteristics of the actual economy and, at the same time, is simple enough
for the instructor to feel that he fully understands its behavior. To achieve this
goal I believe that, if at all possible, the instructor should build hxs model
himself, ratner than use one constructed by someone else[5J,

Although construction by each iastruc
hardly facilitates the implementation of
solves any problems for those who have
that Professor Holbrooks recommendation
to construct a set of computerized
economic theory courses. The game models
mechanisms, and to have similar input
student. Rather than design models to nee
construct the models to feature options
structure the models to permit progressi
of complexity desired by the instructo
the models in a stepwise fashion after st
previously added feature.

tor of a model with j
ceteris paribus method
little or no backgrou
for self-enlightenment
game models designed
were intended to cove
and output formats for
t some acceptable leve
for varying degrees of
on from relatively sin
r. The method used wa
udents had been given

ust the right level of complexity
ology as a teaching device, or
nd in computer science, I decided
was worthy of pursuit. I set out
explicitly for use in a number of
r a wide variety of economic
ease of use by the instructor or
1 of complexity, I attempted to
complexity. The objective was to
pie contexts to almost any level
s to admit additional features to
an opportunity to master each

In addition to the
The sa models permit the
terminals (or with a
effects of changing one
change. Since the si
they may be use d by stu
Thus, the simulation
methodology as a teachi
variables in a rarifi
with experience in mani
the complexity of the r

game models, several simulation or demonstration model
instructor to demonstrate in the classroom with
n opaque or overhead projector to illustrate previous
or as many of the variables in the model as the inst
mulation models are designed to reflect the variables i
den*:s to test the effects of variable changes prior to
mocels provide the vehicles for implementing the
ng device. The simulation models permit the stude
ed atmosphere of constant conditions; the game models p
pulati.ig the variables under conditions of interdepen
eal wjrld.

s were structured.

remote computer
computer runs) the
ructor wishes to
n the game models,
game decisions,
ceteris pa rqbus
nt to aanipulate
rovide the student
dence approaching

While the desire to develop adequate programs for use in microeconomic theory courses
provided the initial impetus for the developmental effort, it became apparent at an early stage
in planning that an extension beyond the micro theory of the firm would be useful to the

ERIC

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162

instructor who is concerned with both the micro and macro aspects ot the economy. Thus, general
equilibrium and macro programs have been added to the initial micro theory programs. To date,
fifteen different game and simulation models have been designed, and most have been used in
various economics courses at Furman University during the last two years. The programs are
written in the FORTRAN IV computer language for use on an IBM 1130 computer installation with an
18K memory core capacity and disk-pack data storage. The programs may be adpated to other
computet installations with relative ease, and to computers with smaller core capacities by
reducing the number of firms, products, market areas, or countries for which the variables are
d ime nsioned •

Section III

The programs are grouped into three categories: the microeconomic context, the general
equilibrium context, and the macroeconomic context, rt ic roeconom i c theory generally concentrates
attention on the behavior of indvidual units in the economy - the consumer, the producer, the
resource owner, and the resource employer. The first two programs in the micro series are
designed to permit instructor demonstration or student simulation of the effects ot changes ot
any of the determinants of demand or supply in commodity or resource markets. The next three
programs are designed for instructor demonstration or student simulation of the effects ot
variable changes, respectively, in the marketing-mix control of an imperfectly competitive
t i r m * s demand function, inventory control by the firm, and the firm's control ot its production
function. In any of these five programs, the instructor may use his ceteris paribus methodology
to change only one variable at a time to illustrate results, students may use the same five
programs to simulate the effects of variable adjustments in advance of game decisions.

Following the five teaching or simulation models in the micro series are three game context
models which are designed to be used in sequence to effect a progression from a relatively simple
context to more complex situations. The first model is that of an oligopoly[6] context
dis tr lbu tor-oeha vior game. This model simulates the operation of firms in a single product,
wholesale or retail level oligopolistic market structure, with no manufacturing. The objective
of this model is to permit the student to develop his understanding* ot, and skill in
manipulating, the basic marketing-mix and inventory control variables under conditions of
competitive oligopolistic interdependence. An option permits tne instructor to limit the
students to a single advertising type, or to make available to the students any of a wide range
of mar keti ng- mi x va riaoles - new s pa per , magazine, radio, and television advertising; promotion
type; package type and color; and product service and development expenditures. The program is
designed to handle any number of firms (limited by tne memory core capacity of the computer
installation used), and to be played for an indefinite number of time periods, usually described
as the quarter. Time lags are limited to one quarter, and data may be carried forward from each
quarter to the next on punched cards, disk files, or tape files. Tne print-out includes decision
listings; cost, revenue, and profit statements; and a balance sheet.

Two other game programs ire extensions of the one described above to permit the student to
integrate into manufacturing, to take an additional product line, and to extend marketing and
manufacturing operations into other geographical areas. The three game models may De sequenced
in tne sense that time- lagged data from the distributor model for any quarter may be read as
part of the input data for the manufacturing model for the next quarter; data from either the
manufacturing or the distributor model may similarly be read into tne multiple product and
market model.

The use of the three game programs in sequence permits the instructor to introduce his
students into the firm operation at the simplest level of single product distribution in a
single market area with a minimum of advertising types. Once the students have been given an
opportunity to operate the firm at this level, the instructor may permit them to progress as tar
and as rapidly as he deems desirable into marketing-mix expansion, manufacturing, other product
lines, and other geographical areas (including warehousing, distribution, and manufacturing
functions) •

The five simulation models may be used by students in conjunction with any of the three
game models to simulate the effects of variable changes in advance of game decisions. Thus, the
student may reduce his complex game problem to its elements in the simulation models to "pin-
down" tne behavior of each of the variables separately, or several together. His problem, then,
is to take the ceteris £aribus knowledge gained from the simulation models, and apply it in the
interdependence context of the game r.odels. He thus has the opportunity to work with each
vananle separately in a rarified atmosphere, and all variables together in a context which more
closely approaches the real world.

There are three general equilibrium models, one of which is purely for teac ling purposes,
the other two ot which may in concept be sequenced with the game models of the micro context.
Insertion of th*7 general equilibrium models between the micro and macro context models permits a
natural transition from the micro to the macro. This is accomplished in concept by aggregating

• i

174

163

tha tins ot the micro context into sectors by types of con rood i ties produced. The transition
from general equilibrium to the macro context is accomplished m concept by aggregating the
various sectors of the jenoral equilibrium context into the business sector ot the macro
con te x t.

The teaching model of the general equilibrium context is an input-output table program
which may be used by the instructor to demonstrate, or by the student to simulate, the effects
of sector independence within a nation as the inputs in one or more sectors are changed. The
program format includes a 10 by 10 sector input-output array.

The general equilibrium context includes two game models wnich differ according to the
difference between interregional and international trade theory. The interregional trade model
is i three region, three produce, three resource comparative advantage program. The program
features interregional commodity and resource flows induced by wage and price differentials
between the regions. The rational operation by students of the nondurable consumer goods,
durable consumer goods, and capital goods sectors in the various regions permits demonstration
of regional comparative advantage production specialization, commodity and resource pne*?
equalization across regions dua to resource and commodity flows, and industry relocation across
the reqions.

The international trade model differs from the interregional trade model only in that
studants are constituted as operators of the productive capacities in countries rather than
regions, and i n ter na t iona 1 resource flows are prohibited. Student operation ot the countries in
this program permits demonstration of international comparative advantage specialization, and
the 3t oipe r-Sa muel son hypothesis (resource prices tend to be equilibrated across national
boundaries due to international trade in commodities, even thougn the international movement ot
resources is prohibited).

The macro context includes four teaching or simulation programs, and one game program which
has three complexity options. The four teaching programs are designed to fit the national
income accounting, commercial banking system, Keynesian macro variable, and Harrod-Domar
econamic growth contexts. Each of these programs may be used in the classroom by the instructor
to demonstrate the effects of ceteris paribus or multiple variable changes, or by the student to
simulate the effects of variable changes in advance of game decisions.

The macro game program provides for student participation as operators ot the consumer
(resource owner), business (resource employer), banking, and government sectors of the economy.
The program can handle any number of countries in operation at any one time (limited by the
memory core capacity of the computer installation used), and can be played for in indefinite
nurabar of time periods. The program features complexity options which permit the instructor to
introduce his students to the macro variables in a closed economy without government, and then
progress to admit government to the model, and open the economies to international trade. The
open-economy option features international commodity trade generated by price and incone
effects, autonomous capital flows generated by interest rate differentials, compensatory capital
flows, automatic exchange rate devaluation if the country voids itself of foreign exchange,
discretionary exchange rate revaluation, and tariff and quota limitations on imports.

Section IV

Within the last two y?ars four of the micro teaching programs and the three micro game
programs have been used in intermediate m icroeconomic theory courses at Furman University. One
of the teaching models, the resource market program, is still in the developmental stage. The
seven extant programs have been used to accompany a standard intermediate microeconomic theory
t ext' 7 ].

The macroeconomic game program, and two of the macro teaching programs have been used for
two years in intermediate macroeconomic theory courses at Furman to accompany a standard
intermediate macro theory text] 8]. The national income accounting and the economic growth models
are still in the developmental stage. The open-economy option of the macro game, and the
international comparative advantage general equilibrium program have been used in international
trade courses at Furman.

The results of program use are reported as objectively as possible below:

a. First, the results have shown no significant quantitative gains as yet. Although no
less textbook material has been covered while using the programs than previously, it
is not yet possible to report being able to cover more material. There is a very
important reason for this. During the last two years while the programs have been in
the developmental stage, the students have been acting as the guinea pigs. They have
found the "bugs" in both the economic models and the computer programs as the

164

*75

programs were being used- "Debugging'1 in this Banner necessarily slows down progress
in the game contexts as rounds of decisions must be delayed teaporanly while repairs
are accomplished. Thus, it will not be surpLising to find, when most of the "bugs"
have been deleted, that some more can be a ccomp 1 is lied in each course as the programs

are administered more smoothly. Meanwhile, the programs are being thoroughly

classroom tested.

b. The positive gains which can be repotted at this time are qualitative in nature. It

is my judgment that my students attain a much better grasp ot the text material when
they use the simulation programs and participate in the game contexts than they did
before the use of such programs. The evidence of this i*s found in the types and
degree of sophistication of questions which they are led to ask as a result ot model
use or game pa r t i c ip a 1 1 on . Use of the simulation models permits the student to
"ureak-down" a complex problem into its elements for ceteris paribus treatment.
Participation in the game contexts forces the student to pull together the

information from all of his previous dnd current coursework in the economics and

business atea it he is to compete success t u 1 1 y . And by use of the simulation models,
no can solve or gain insight into many of the gdme problems by himself.

c. The extant prog Tans seem to have gone d long way toward preventing the frustration
which I have witnessed on the parts of students ensnared m the hy per -com plex i t y ot
some available game models. The models described above, designed for sequential and
mutually supporting use, permit a gradudl approach to the complexity ot the real
world as the instructor begins his students at a relatively simple level ot analysis,
dnd progressively aids features to the gdme models.

Tne results reported above are nearly all non- nega t i ve . There are ot course possible
negative efrocts from the use of computerized game models in the classroom- First, the
instructor and the students miy become enamored with the use of the machinery, whether positive
results are forthcoming or not. Second, there is dlways the danger thdt the instructor will
permit his students to fall into the trap of "game-playing, “ rather than simulating rational
real-world behavior. Third, there is the danger that the student will take with him the
misconception that the Complexity of the real world easily may be decomposed into its uniquely
identifiable elements, as in tne simulation models. Fourth, tnere is the possibility that the
instructor will permit ;iis students to play and become bogged down in the game, to the exclusion
ot text material whicn should have been covered.

The model designers, tie computer programmers, dnd the writers of text mateiial to
iccoapany the models may try very hard to prevent dll of the negative effects described dbovc.
But responsibility for preventing those negative effects ultimately rests upon the shoulders ot
the program a dmi n i st ra tor and instructor in the classroom. The instructor must be ever vigilant,
lest tie or r.is students tall into any of those traps.

In conclusion, I have found that the combined use ol the sequential game models with the
mutually supporting simulation models dS described herein can provide the instructor with a
nijhiy productive set of teaching devices, provided thdt the instructor will take pains to
prevent tne negative effects mentioned above.

FOOTNOTES

1. rtouert S. Holbrook, "The Use of Economic Policy Games as an Aid to Student Understanding,"

of a Conference on Computers in the Undergra d ua te Curricula, June 16- Id, 19 70,
(Iowa City, Iowa: Center for Conferences and Institutes, The University of Iowa, 1970), p.
5. 13.

2. I have arrived at these conclusion*; after examining numerous available program models, and
having participated in giving oral examinations to students in senior-level business policy
courses in which d quite complex game model was used.

3. The procedure to this point may be described as that of the extreme aprionst, one who
declines to test conclusions on grounds that they must be true in an a priori sense it
logical reasoning flowed from accepted premises.

4. it the analyst tests hi3 conclusions with ceal-world data, ms procedure may be described
as thdt of the logical positivist.

6. Holbrook, op. cit., p. 5-13.

6. The term "oligopoly" is used in economic analysis to describe d market structure with few
enough tirras so thdt thera is a significant behdvior interdependence. Each firm can

°f an0tbeC and the aCt0C* 8eacti°"s can likewxse be felt an*
^Honewood° ^ ** Kei'9US°D' tofittMMMifi KlttEI
fork : McGraw-Hill, SX).1* that ^ T* *' Deinbec5 and D* "• "CDougall. Nactaeconoaiss (New

166 177

i) > 5

AN UNDERGRADUATE COfl PUTEB- ASSI STED INSTRUCTION COURSE IN
THE EARLY IDENTIFICATION OF HANDICAPPED CHILDREN

G. PhilLip Cartwright and Carol A. Cartwright
The Pennsylvania state University
University Park, Pennsylvania 16802
Telephone; (814) 865-0471

iQ^E^uct ion

Under grant support from the Bureau of Education for the Handicapped, and the Bureau ot
Educational Personnel Development, U. S. O, E, , personnel at The Pennsylvania state University
have developed a computer-assisted instruction course in special education. The course called
CARE (Computer Assisted Remedial Education) is a completely self-contained three-credit college-
level com pu ter-assisted instruction (CAI) course which deals with the identification of
handicapping conditions in children. The purpose of CARt is to give students in preschool and
primary education curricula the knowledge and skills necessary to identify children who
otherwise might be educationally retarded by the age of nine or ten. The course is designed to
promote clinical sensitivity on th'B part of the students and develop in :hem a diagnostic
awareness and understanding of the strengths and weaknesses of handicapped and normal children.
Undergraduate students who complete the 30-hour course will be able to evaluate systemat ically
children1 ; learning potential and to formulate appropriate educational plans for the children.
Three credits in the Penn State course EEC 400: Introduction to Exceptional Children is given
for successful completion of the course. The course is taught completely by compu te r-ass isted
instruction.

Need

This project seeks to improve the quality of teacher preparation in the area of special
education. Intensive training in special education concepts is directed primarily toward
prospective classroom teachers of elementary grades in rural schools in Pennsylvania* s sparsely
populated counties. A high proportion of the children in these counties cone from low-income
families who must depend heavily upon their local schools for long-term support and escape froa
poverty. The situation in Pennsylvania’s Appalachian region reflects a pressing national meed
for special education provisions. It has been estimated that 3., 75 million of the nation*s six
million handicapped children are not receiving the special services they need. The absolute
level of this lack of service is relatively more severe in schools .serving the rural population
than in the ur^an and subULban center t. The present rates of preparation of special education
personnel are not sufficient to diminish the gap between needs and delivered services. It should
be obvious that an alternative, or at least an augmented approach to the provision of special
services to atypical children must be undertaken. An alternative is illustrated in this project:
preparation of teachers of elementary and preschool children to identify ar.d deal effectively
with conditions in children which may adversely affect their school performance.

Specialists in early childhood education and special education continually stress the need
for early diagnosis of educational or behavioral deviancy, followed by early intervention with
programs designed to promote cognitive and social development, in order to help handicapped and
disadvantaged children get off to a good start in life. It is the contention of these
specialists that the early years of a child’s life are extremely important in terms of
personality developme.it and intellectual development. Unfortunately, most preschool and primary
level teachers have not been trained specifically to identify children who are handicapped or
who exhiDit behavior which may be symptomatic of future educational difficulties.

Purpose of CARE

The purpose of the course called Computer Assisted Remedial Education (CARE) is to give
educational personnel the knowledge and skills’’ necessary to deal effectively with children who
have educational problems.

)

The CARE course is designed to prepare prospective preschool and primary level elementary
teachers and other interested persons to know the characteristics of, and be able to identify,
handicapped children. handicapped children are defined, for purposes of this project, to ba
those children who hav' atypical conditions or characteristics which have relevance for
educational programming. Handicapped children include children who display deviations from
normal behavior in any of the following domains: (a) cognitive, (b) affective, and (c)

psych onto tor •

The philosophy of the course is such that teachers are encouraged to look at children as
individuals. The use of traditional categories or labels is minimal. However, certain terms and

167

concepts related to ha ndicapping conditions are taught so that persons who tar.e this course mre
better able to comraunica te with other professionals in the field.

Off-line Materials Used in CAhE

when a student is interacting with \ he computer assisted instruction (Chi) system, he is
said to be working "on-line. * On-line instruction in the CARE cours is dependent upon
additional aateriils which ^re r.ot controlled oy, nor lccessible to the computer system. These
materials are called "off-line" materials; they play a l'rge and very important role in the
course.

CARE Uilldbook. The CAKE Handbook was written especially for the CAHE course. The book is
4^0 pages in length and contains a JbO-itea glossary of terms used in the course. It has two

functions. First, the Handbook is a detailed summary of the course material. It jay ,be used as a

reference or refresher after a student has completed the course of instruction. Second, the

Handbook contains reference material to which the student must refer when he is working on-line.
The reference material consists of charts, tables, student cumulative records, examples of

evaluation devices, definitions, and many other kinds of information. Thr Handbook also senes
as a readily available notebook in which students make notes of important points.

Specimen tests. The appropriate usage of three screening tests is taught. The three tests
are the Denver Developmental Scree n in g Test, the Metropolitan Readiness Tests , and tLa First
Grade Screening Test. These tests were designed to be used by teachers and others who have mot
received extensive training in testing. Each participant in the project receives sets of all
three instilments. Actual test administration is simulated and problem areas pointed out.
Teachers are asked to score and interpret results of the simulated administrations.

Textbook. The textbook used as a supplement to the course is:

Smith, R. M • (ed.) . Teacher Diagnosis of Educational Difficulties. Columbus, Ohio:

Charles E. Merrill 1969.

Ob ject i ves

Upon completion of the CAI course, participants will have achieved the following
objectives, which are directly correlated with the decision process flowchart shown in Figure 1.
Participants will:

A. know the characteristics of handicapped children ind be aware of symptoms which are
indicative of potential learning problems,

B. be able to screen all children in regular classroom programs for deviations and

determine the extent of the in ter-indi vid ual differences.

C. be able to select and use for those children with deviations appropriate connerical
and teacher-constructed appraisal and diagnostic procedures in order to obtain more
precise information as to the nature of the deviation.

D. . be able to synthesize information by preparing individual profiles of each child's

strengths and weaknesses on educationally relevant variables.

E. be able to evaluate the adequacy of the information available in order to make

appropriate decisions about referral to specialists.

F. be able to prepare adequate documentation for the case if the decision to refc>r is

alfirmati ve.

It is expected that the teachers who exhibit the competencies listed above will
systematically evaluate children's learning potential and formulate appropriate educational
plans accotding to the decision process outlined in the following section.

Relationship between objectives and the decision process. The six objectives are directly
associated with the first six steps (boxes) in the derision process. The first two steps in the
decision process dictate that the teacher evaluate all the children in the classroom in order to
identify those children who exhibit deviations from normal behavior. Objectives A and B are
related to the first and second steps in the decision process.

Evaluation should be thought of as a continuous process which is an integral part of the
total educational process. The evaluation process includes two major tasks: (a) obtaining both

quantitative (numerical) and qualitative (categorical) data about children's abilities in the
cognitive, affective, and psychoaotor domains, and (b) making value judgments about these data.
To identify children who exhibit deviations from normal expectations is to make a value judgment
that a particular behavior is considerably different from that which is displayed by a majority

►

Continually evaluate all children In order to
Identify children with deviations from normal
expectations. ,

Objective A

Gather more precise Information about the
nature and the extent of the deviations.
Objective C

(Modify the child's
educational program or
the basis of Infor-
nation obtained.)

6. Prepare adequate documentation and make the
appropriate referral.

Objective F

*Th1s step Is the subject of a CAI course to be developed.

FIGURE 1 . Decision Process

180

of the child's chronological age peers and is, therefore, different from the behavior usually
expected of children in that age group.

In order to sake appropriate educational judgments (i.e. , judgments which result in
educational planning aimed at intervention for the purpose of preventing potential learning
problems, correcting existing learning problems, or enhancing learning assets) , teachers need
inforaation about the atypical conditions and characteristics which are likely to he present, to
soae degree, conditions and characteristics which are likely to he present, to sole degree, in
groups of school age children. Inforaation concerning both noraal behavior and possible ahnoraal
behavior in each of the doaains (cognitive, affective, and psychoaotor) is the prerequisite for
the task of screening children in teras of deviations. It is assuaed that injfervice teachers
possess adequate knowledge concerning noraal hehavior and operate, in general, with expectations
of noraal behavior for the children in their classrooas. The investigators aaintain that the
majority of inservice teachers have not had an opportunity to acquire extensive inforaation
about possible deviations, or abnoraa lities, in behavior which influence learning. Therefore,
course content used in association with objective A provides the basic inforaation which is the
prerequisite for the screening task (steps one and two) and for subsequent tasks in the decision
process.

The following itens are exaaples of the course content for objective A: (a) definitions of
atypical children, (b) descriptions of various groups of atypical children such as aentally
retarded and eaotionally disturbed children; (c) descriptions of children with speech, aotor,
auditory, and visual problems; and (d) justification for the use of certain variables in
describing atypical children. Sinoe the course is intended for teachers working with preschool
and priuauy level children who nay not yet manifest clear-cut signs of atypical hehavior,
teachers are given inforaation relative to the lore subtle clues to incipient prohleas.

Acquisition of the prerequisite inforaation allows the teacher to identify or screen oat,
those children who exhibit deviations froa noraal hehavior. Achieveaent of objective B enables
the teacher to aake correct use of data which are usually readily available to classrooa
teachers. Course content directed toward objective B focuses on the following: (a)~the relative
nature of normality in teras of socio-cultural factors, and societal and educational
expectations, (b) inter- and in tra- individual differences; <c) interpretation of inforaation
which is generally available for all children in the group such as results of group
intelligence, readiness, and achievement tests, questionnaire responses concerning hoae and
family, and so forth, and (d) the continuous and circular nature of the screening process.

During the first phase of the decision process, the teacher surveys the entire group of
children for performance on certain relevant variables in order to select those individual
children who exhibit deviations of a sufficient degree to warrant wore intensive diagnosis, with
the completion of the screening at any one tine, the teacher will have formulated ’'suspicions*
or hypotheses about soae of the children in the group and will proceed to the third step in the
decision process for these children. It should be noted that the teacher would continue to use
the screening process as new group data become available.

During the third step in the decision process, the teacher gathers precise information
concerning the nature and the extent of each individual child's deviation. Objective C is
associated with this step. At this point, the teacher adds information about each child’s intra-
individual differences to that previously obtained (in the first step) about the inter-in
dividual differences. The teacher needs to obtain data concerning discrepancies within the
individual’s growth pattern (the child’s specific abilities and disabilities) for each of the
children selected during the screening process.

Achieveaent of objective r enables the teacher to perform at the third stage of decision
making. Course content for ohje ve C includes: (a) rationale for use of a variety of
appraisal procedures, (b) us f commercially prepared tests and non-testing materials; fc)
techniques of constructing and using teacher-made tests and non- testing procedures, both formal
and informal, (d) criteria for selection of appraisal procedures with emphasis on validity and
reliability relative to a variety of purposes; (e) sources of information about the child from
other individuals, such as peers and parents; (f) use of day-to-day informal situations, devised
by the teacher, to yield inforaation about attainment of specific behaviors of interest. The
emphasis at step three of the decision process, and for objective C, is on individualizing
appraisal for each child in terms of the deviations noted during screening. The teacher seeks
information in addition to that which is usually available for all children, and this
inforaation will be unique to the deviation for which the child was screened out of the total
group.

Tentative coapletion of the third stage in th«r decision process, together with achievement
of objectives D and E, enables the teacher to evaluate the comprehensiveness of the obtained data
and, therefore, aake the decisions required in steps four and five. Course content associated
with objective D includes: (a) description of profile charts and related diagrams, (h)
procedures for selecting certain variables for inclusion in an individu- l’s profile, (c)

interpretation of normative data; <d) rationale for the usr of various kinds of information,
troi a variety of sources, in combination; and (e) techniques of constructing and using profile
charts and colated diagrams. Course content for objective E consists of: (a) criteria for

determining the comprehensiveness of the obtained data; (b) information concerning the
specialists who can De expected to provide various types of intensive diagnostic services for
children, and (c) descriptions of the classroom teacher's role in relation to the roles of
various specialists.

If the teacher makes a negative decision at step four, he needs to return to step three and
collect the information required to complete the child's profile chart before proceeding through
to step five. However, if the teacher is able to make an affirmative decision at step four, he
will* proceed immediately to the next decision block, which is step five in the process.

In formulating an answer to the question posed at step five, the teacher asks himself: Have
I exhausted all sources of information available to me in ay role as a classroom teacher? Can 1
make educational plans for this child on the basis of information currently available? Do I need
more information before making educational plans for this child?

If the decision at step five is for referral, the teacher will proceed to step six.
Objective P is related to step six. Course content associated with step six includes (a)
criteria for selecting the appropriate specialist for various types of referrals, (b) procedures
to be used in documenting the request for referral, (c) descriptions of general procedures to be
followed in making referrals, (d) activities which might be required of the teacher subsequent to
requesting a referral, and (e) feedback to be expected by the teacher relative to disposition of
the referral.

If the decision for referral at step five is negative, the teacher will be responsible tor
modification of the child's educational program within the regular classroom setting (step seven
in the decision process). It is not possible in this one course to deal with extensive
modification of programs. A second course is planned to cover this problem. Modification of
programs for atypical children would include the following topics: (a) techniques of effective
classroom management, (b) specialized teaching strategies which might be used for amelioration
of difficulties, or for enrichment, in various subject-matter areas, (c) special materials to be
used in association with specific strategies, (d) sources of information regarding specialized
strategies and materials, and (e) resource persons usually available to assist classroom
teachers.

Com pu te c- Assisted Instruction

Instruction is individualized for the teachers by means of computer-assisted instruction
(CAI ) • CAI presents instruction in an environment where the material presented to the learner is
selected and sequenced, with the aid of a computer, to be responsive to the individual learner's
needs. The computer selects sequences of instruction which are appropriate to an individual's
background knowledge of the course content, his rate of progress through the material, and the
types of errors (or non-errors!) the student makes as he interacts with the system.

Because each student can communicate with the system independently, and since the computer
can arcive at logical decisions based on its analysis of incoming student performance data, the
capability exists for the intelligent adaption of instruction for each student. The logical
decision-making ability of the computer, along with its extremely rapid access to larae volumes
of stored information, combined with the knowledge and skill of the author-programmer, can
provide for a wide variety of individual differences among learners.

To accomplish the course objectives outlined above, an 8-terminal IBM 1500 Instructional
System has been installed in the Computer Assisted Instruction Laboratory at Penn State. The IBM
1500 Instructional System consists of eight instructional stations each with cathode-ray tube
display, light pen, typewriter keyboard, audio device, and image projector. The computer
equipment is comprised of an 1131 central processing unit, 1442 card reader and punch, 1133
multiplexer control unit, two 2310 disk storage drives, 1502 station control, two 1518
typewriters, and two 2415 tape drives#

The central processor of the IBM 1500 Instructional System is an IBM 1130 computer with
32,768 sixtetu bit words of core storage. In addition to the usual peripheral equipment, the
central processor depends upon three IBM 2310 disk drives <1,436,000 words) for the storage of
usable course information and operating instruct'* ~. Twin magnetic tape drives record the in-
teraction between the program and the studer for later analysis and coarse revision. Core
storage cycle time is 3.6 microseconds and read/wrx e time for disk storage is 27.8 microseconds
per word.

Each IBM 1500 student station consists of four optional display/response devices which may
be used individually or in combination. The central instrument connected to the computer

• i

171 .

consists of a cathode-ra) tube screen with si
for a total of 640 display positions. Informatio
micro-seconds from an internal random access
respond to displayed letters, figures, and graph
screen. A part of the CRT device is the typewrit
learner to construct responses, have then displa
screen, and receive rapid feedback in the for
128 characters each of the course author*s own d
projector loaded with a 16mm microfilm is capabl
accessing forty images per second under program
four channels on a 1/4-inch tape is an inteqr
the system is a separate device which enables th
about students and course progress. Figure
photograph of a student working at the CAI terai

xteen horizontal rows and forty vertical coluins
n sufficient to till the screen is available in
disk. A light pen device enables the learner to
ics by touching the appropriate place on the
er-like keyboard which lakes it possible for the
yed at any author-desired point on the CRT
■ of an evaluative aessage. Four dictionaries of
esign can be used simul taneousl y. An iiage
e of holding 1000 images on a single roll and of
control. An audio play/record device based on
al part of the systea. An electric typewriter on
e proctor to receive a paper copy of information
2 shows the systea configuration. Figure J is a
nal.

Evaluation

£2£CL§.liv£ evaluation. Several course revision cycles involving 400 students were used in
the format!ve~e valuation phase of this project. Student performance records were obtained by
leans of an automatic recording system. The syste* records data such as exact responses tor each
frame and course segment, number of requests for help, time of response, response latency,
number of attempts made by each student to each question, correctness or incorrectness of
response, type of response required, contents of displays and registers, and other similar data.
Data of this nature are invaluable in diagnosing errors in content or logic and in evaluating
the extent to which students are reaching each of the 1100 sub-objectives of the course.

A total of 333,018 separate student responses were analyzed and extensive revisions were
made on the basis of the analysis. Each of the revision cycles resulted in noticeable
improvements in student performances.

Suimative evaluation. During the Winter Term, 1971, a suomative evaluation of the CARE 1
program was made. All students who were enrolled in EEC 400: Int rgductign to the Education of
Exceptional Children were randomly assigned to either of two cond it ions - Compu ter- Assisted
Instruction (CAI) ~or Conventional Instruction (Cl). The CAI group (n = 27) received all
instruction by means of the IBfl 1500 Instructional System and did not attend classes with the Cl
group. The Cl group (n = 87) received the conventional lecture-discussion method of instruction
and met three days per week in 75 minute sessions for ten weeks.

All students, CAI and Cl, were enrolled as regular students for three credits of
undergraduate or graduate credit. Doth the CAI and the Cl courses were designed to reach the
same objectives. The instructor of the Cl group was an author of the CAI course and helped plan
the structure and the objectives of the CAI course.

The Ldpendent variables in this investigation were time and final examination scores based
on 75 items. Results are shown in Table 1.

Final

Examination Scores

S.D. t

Computer-Assisted Instruction

65.69

4.68

Conventional Instruction

52.78

5.89 11 .65*

♦This difference Is statistically significant with p < .001.

Time

Computer-Assisted Instruction 7 * 25.21 hojrs per student

Conventional Instruction 37.5 scheduled hours

per student

TABLE 1. Results of Suimnative Evaluation

183

Wi *

172

►

ERIC

FIGURE 2. Configuration of the IBM 1500 Instructional System.

y *

184

173

FIGURE 3. Student working at a CAI terminal.

174

These data indicate that the group of students instructed by CAI obtained a lean score ^4%
higher on the final examination than students instructed in the conventional Banner.
Fu rt her Bore , the CAI students completed the three-credit course in 12 hours less tile (33%) than
the conventionally instructed students.

Nodes of Instruction by, CAI

The CARE course uses a wide variety of instructional strategies to assist students in
reaching the course objectives. All the strategies are interactive and all require active
involvement on the part of the learner. The lost prevalent strategy used in the course is the
approach. This approach simulates the master tutor engaging in an interactive dialog
with an individual student. The tutor presents information, asks penetrating questions, and
carefully analyzes the student's responses to the questions. On the basis ot the student's
demonstrated understanding or lack of understanding of a given concept, the tutor provides
alternative courses of instruction, remedial sequences of instruction, or even enrichient
material. The tutor can move a capable or well-informed student through a course of instruction
very rapidly. Similarly, the tutor can tailor a sequence ot instruction to meet the needs of a
student who is not as capable or does not have a good background of experiences or preparation.
The sophisticated CAI system can perform the chores of dozens of tutors rapidly and efficiently.
The net effect is that hundreds of teachers in the CASE project have been individually tutored
in certain special education skills.

The second major m ode ot instruction used in the CARE course is the inquiry approach. This
type ot activity is used in the latter stages of the course to draw together all the concepts
acquired by the students throughout the course. This strategy includes simu la ti on of regular

classroom problems as well. In essence, the inquiry and simulation approaches as used in the

CARE course are directed problem solving strategies. Students are told that they have access to
information about a class of first-grade children. One or lore of the children in the class may
be handicapped or have an educational problem of one kind or another. It is the student's task,
in effect, to screen the class for children with educational problems, identify those children
with potential or existing problems, and 4eal with the problem by modifying the child's
educational program or making an appropriate referral. The student begins the screening by
looking over the complete cumulative records of the children in the class. The student nay ask
the computer for additional information. Not all the information the student receives is
accurate; in fact, many false leads are given to lure the unwary student into naking the wrong

decision. The computer system will lead a student down the wrong path for awhile and then

explain why that particular line of reasoning is not approprie .e for that specific child.
Eventually, as a result of skillful questioning on the part of the CAI system coupled with the

appropriate line ot questioning by the student a decision is reached by the student to refer a

child or to modify the child's program. The student's decision is evaluated by the systei and

then the student's plan for referral or program modification is evaluated by the CAI systei.

When a student completes the course, he has actually constructed several case histories of
children .'ith problems and has made educational decisions related to the best plans for dealing
with these problems.

166

175

1S75

ERIC

176

Problem: Imagina ive flight form

PREPARING MATHEMATICS TEACHERS TO USE
THE COMPUTER IN SECONDARY SCHOOLS

Roger H. Geesiin
University of Louisville
Louisville, Kentucky 40208
Telephone: (502) 636-4584

ABSTRACT

After a brief introduction which includes some background natenil, the pa^ei deals with
three major areas: the description of a course to prepare teachers, an indication oi what to
expect when the computer is introduced into the schools, and one approach to solving the problem
of high coaputing costs. Finally, there are some general concluding remarks.

In t roduc tion

This paper is based on experience gained over the past two years in an experimental program
developed at the University of Louisville in cooperation with the Louisville and J .fferson
County Public Schools, '"his program will be expanded and stre ng then** 1 through an NSF sponsored
Cooperative College School Science program which will begin on July 3, 1972, with six-week
suoier institute. The course described here was also offered in the Spring term, 1972, so that
any significant differences between this and a concentrated summer course may be noted in the
talk. Discussion of the computer network in use will be postponed to the portion dealing with
this and other practical matters.

There is something quite unusual about using the computer in any kind of teaching, and it
is for this reason I have avoided the word " * r aini ng" in the title of the paper. Teachers can be
trained to use the overhead, movie and slide projectors. They can learn to use effectively all
kinds of audio-visual aids, and I would interject here that secondary teachers seem to do a much
better job at this than their counterparts in the universities and colleges. But the computer is
not just another teaching aid, to be used by the better teachers and ignored by the rest. I hope
to clacify the importance of a special effort to pre pare teachers to use the computer
effectively.

Let us look briefly at the computer, which in most time-sharing systems is present in the
form of a teletype or other terminal device. Since all who attend this conference are, or should
be, familiar with the distinct advantage of an interactive time-sharing environment over batch
processing for beginning instructional purposes, I will not present that discussion here.
However, in this paper I shall normally use the word computer to mean a time-sharing computer
terminal wh.* ~*h has available at least one easily learned programming language, such as one of
the extensions of BASIC. What is the nature of the beast, other than being a somewhat noisy but
speedy communication device which will become quieter and faster as technology and funds permit?

The versatility and power of the computer puts it in a class by itself as a teaching aid. It
can give individual remedial drill to a pupil without the attention of the teacher. The pupil
can himself make up problems and then "check*1 the computer (more on this later). The average
student can use it to supplement his course work, giving clearer insight into concepts to ue
learned and allowing him to solve problems more realistic and complicated than otherwise would
be possible. The advanced pupil can explore, create, and experiment in the many fascinating
areas of mathematics which lie beyond the normal and advanced secondary courses. Note carefully,
this single piece of equipment can catch the attention of the slowest learners and give them
some success in a subject they have failed for as long as they can remember. And tne next moment
it provides the means of carrying out long involved computations over elaborate logical paths in
some MnewM area, yet unexplored by student or teacher.

These remarks should » enough to hint at the potential of the computer in math mat cs
teaching. Let us see now how ».e go about preparing the teacher for this adventure.

The Introdgctory Course

Various aspects of a three semester hour course open to both senior college undergraduates
and graduate students will be described here in general terms as a frame of reference. The
details will vary from offering to offering since much depends on the interests of the class.

The course description is as follows;

188

Hath

595

The Computer n flathematics Teaching (3j
Prerequisite: One year of calculus
{no prior computer experience needed).

Introductory programing and the use
of the computer in teaching a wide tinge
of topics in secondary school
mathematics. Sumer session.

Note that the prerequisite should not exclude any secondary school iatheiatics teacher, and
reassurance is given to those having no experience in computing. It is very helpful if the
teachers taking the course have actually tauglit, if only in a student teaching experience, but
when the course is taken by undergraduates this may not be possible

The course has three lain objectives: to develop programming skill adeq^.e for ieaningful
use, to sa^n significant experience in problem solving and other areas of interest to each
teacher, and to r^q -ire each teacher to give careful consideration to the way he will introduce
the use of the computer into his own teaching in a particular school situation.

The first goal can be easily accotplishod by neginning BASIC with hands-on experience the
first or second period at the latest. Adding PUNT statements to existing programs encourages
providing ieaningful output froa the run of a prograi, and this carries over nicely to the
program; written independently later. At the beginning, lost teachers have no idea how they
would ise the computer, but usually alter four or five classes, they ua in to want to try
something on their own. Encouraging this interest while answering questio s in class and
laboratory makes for a very stimulating course. Back-up suggestions are helpful when interest
laqs, but these : e not as inportant as keeping in touch with what the class is doing and
sharing items of general interest.

Collecting and reading programs regularly with no fixed number required encourages the
teachers to \o as much as they can, and provides opportunity to suggest improvements which they
can incorporate immediately. Adequate, reliable computing fac.\lities are essential, the more
terminals the better, and hours of availability should be as long as possible. Some teachers
arrived as early as 7 a. a. and others stayed as late as 9 p.m. in order to have longer,
uninterrupted time on the computer. However, normal constraints jay encourage the preparation of
paper tapes to make more efficient use of the on-line terminals. Indeed, if such will be the
case in their own schools, this experience is absolutely necessary. Appreciation tor scheduling
difficulties and other practical problems is gained directly and indirectly through this
exper ience.

Perhaps the most important aspect of the course is the personal experience gained by each
teacher in programming independently. This is the primary opportunity to develop skill in this
area since the students will tend to dominate their school terminal, and the teacher will have
little time to do his own programming after introducing it in his school. So it is vital that
each teacher develop his own ability as much as possible in this brief course, and it is
surprising how competent many become. This experience also brings out two other facts which
should be recognized. The first is that although ability varies, almost anyone can program the
computer and obtain significant results. The second is that they learn more from each other and
actual experience than they learn in the classroom. Both of these should be kept in mind in
developing and evaluating any program.

New topics in programming should be introduced as earlier ones are mastered. As the
teachers become more competent, and interest in their own programs increases, it is time for
them to start organizing their thoughts around their own school situation. For this purpose a
required paper provides an excellent vehicle. It may happen that their situation changes so
drastically that almost nothing they planned is carried out, or they may not have computer
facilities at all. Nevertheless, the careful thought given to this question is never vested.
Here again the range of approaches varies greatly, with none being the right or best way. Each
teacher should find his own approach. Of course, sharing these ideas near the end of the course
may avert some major blunders, but the experience gained in the course gives a very valuable
guide in adapting to changing conditions. When compared fith those having only prior experience
in a programming course, teachers who have coapleted this course appear to have a distinct
advantage because of the relevance of the experience gained to their own teaching situation.

Comments and evaluation of the course by the teachers has been very enthusiastic, and this
enthusiasm has been demonstrated not only by the long hours spent in the course, but by the hard
work and long hours given by them in their schools. It is a demanding but highly rewarding task;
students get excited about their mathematics classes!!

169

When the computer is introduced into the school, many things can happen. I sill indicate a
few effects which ai^ht occur in the classvoow and possible side effects on other student#,
teachers, parents and adainistra tors.

One would expect that the conputer night best be introduced to advanced classes >n senior
Tigh school. This is not necessarily the case, and sone of the nore draaatic results have been
obtained in the basic and general nathenatics courses as early as the seventh grade. This does
not exclude use at the upper levels, but indicates positive results at all levels of secondary
school nathenatics. It is not possible to docusent here the nany cases which support the renarks
that I will sake concerning the various courses and grade levels, but they are based on actual
experience.

.0 the seventh and eighth grades, sotivation can be held high with very sinple programed 3-
tasks. Typing ability is not well developed, but the pupils can denonstrate great patience, both
in typing prograns, and in developing designs to be printed by the cerninal. The random number
function is also popular in the development of gaaes and simulations, giving an intuitive
introduction to probability theory and opening the door to aany experimental uses of the
terminal. A siaple coiu toss prograa can give answers in seconds to a 100* 1000, or even 5000

toss sisulation. The sain point here is that a very aodest introduction to BASIC aud a few

functions can go a long way for this level average or abo*'e average student.

Deserving of special notice is the response by students in the ninth and tenth grade

general or basic aatheaatics classes. Here one confronts pupils who have failed to le*in the
fundasental operations of arithmetic, and expect to fail in auch that they do in any aatheaatics
course they encounter. It is first of all surprising to thea that a teacher would allow thea to
use the computer, especially when soae other advanced classes cannot, lhey guickly respond to

this opportunity to h nve a "status symbol" and pull themselves up fros the bottos of the heap.

The class becomes something special and begins to do its regular work in order to get on the

computer. Suae prefer cot to write programs when given the choice of using the terainal after
their regular work is done or just doing the regular work. But notice that both alternatives
include doing the regular work.

Another specific use in general aatheaatics is to give reaedial drill to chose who have not
learned aulti plica tion, for exaaple. Such a drill can be randouized and personalized with a
grade given at the end, and still be very aodest in oize. Several have been effectively used on
our network and are available to all from our systems library. But even without the drill

program, it was noted in one general math class that the pupils would program a siaple

calculation, and then "check” the cosputer, which to their surprise seesed to be right always.

Here we have the pupil making up his own drill, and working toward the correct answer which
before had always eluded his. The pupil can do either the drill, or this type of calculation
with little or no attention fros the teacher. In basic or general sathesatics classes where the
goals are sost modest, soae remarkable changes in attitude and sotivation can be found as well
as the learning of skills which seesed impossible.

Topics in the upper level courses of algebra, geosetry, trigonometry, probability, plane
and solid analytic geometry, and calculus which lend themselves to treatment on the computer are
leeion. These have been and are being developed and documented in many publications. But a few
general comments should be aade.

Pirst, the students in these upper level courses s?.y resent the intrusion of the computer

on the class time to be devoted to a specific amount of raterisl, and indeed this is a real

problea to be faced by the teacher. The answer may be to have a separate computer course for
senior high students, but such a course for a full semester aay easily take the students beyond
the range of the teacher's computing experience. It is interesting to find that you cannot v
very far in a computing course without running into the need to know aore aatheaatics;
mathematics becomes useful and a part of the real world.

Second, the upper level students are not satisfied with learning the fundamentals of
computing before going on to aore coaplex probleas. They are inclined to jump directly into sose
elaborate, difficult, or even impossible task and then coae to the teacher for help. The teacher
can hopefully convince thea of the need to build a aore solid foundation; a lesson which could
also carry over to other aspects of their lives in preparation for further education. Coupled
with the fact that soae students devote theaselves alaost entirely to writing programs (i.e.
become "computer buas”) at the expense of their other studies, these are ^oae of the
difficulties encountered at the upper levels.

But the benefits seen to outweigh by far the detrimental aspects in the classrooa. One
major gain in all grades (7*12) is the development of skill in logical thinking and in the
analysis of probless. Experience indicates a marked advantage of those with programming
experience in their ability to construct proofs in geometry or to prove trigonometric
identities* The programs written were not necessarily related to the course, but the discipline
of programming itself develops this skill. Students will often go to much greater lengths to

179

satisfy the demands of the computer language for careful logical reasoning than they ever would
to satisfy a teacher.

The time-sharing computer terainal it* the class rooi can be a very strong stimulus to high
aotivation in both students and teachers. Th»^ motivation, which can carry over to mathematics

the driving force behind mu^h of the activity in this
uobieis, there is wide versatility to adapt to uew

and other subject Batter areas, is part c
tield today- There is real power to solve

situations, and there is gr<»at satisfaction m the successful run of every lew prograi

What about the side-effects on those no*, directly involved with the conputer? other
students want to know how they can get to use it, or if they used it last year, why they canft
use it this year; perhaps a computer club would bel[ here. Sole tathetatics teachers aa y feel
threatened. These are just now getting comfortable with the "new tathM and along cones the
computer. Don*t expect inch support or interest iron those not willing to take the preparatory
course.

Parruts also react to the coaputer in the school. But they are proud of the fact that their
chillreo are so interested in anything having to do 'jith studies and have demonstrated a skill
whiev is new and unusual. The response can be even more positive when parents find that they can
also ^earn. I* addition, the equipment for a mathematics or computing lab can take its place
beside uniforas for band or athletic teal, bleachers for the stadium, and other improveaents to
the school worthy of PTA financial support.

School administrators seem to fall
another attack on their meager budgets and t
potential of the computer in the schoo
little or no success. They are convinced tha
into two groups. The one nay invest large am
for trained personnel. The result is what is
Tue final group recognizes the need for
that large sums are necessary to get started
there is pride in the real improvement in th
status symbol. And they find that their inve

into two classes: those that look on the computer as

hose who somehow are convinced of the powerful
Is. The first give little or no support and thus see
t they are right. The second again nust be separated
ounts in computer hardware with little or no support
now a familiar d isi 1 lusionment with the computer,
balance between equipment and trained personnel; not
, but that sufficient funds be used well. Pol' these,
eir educational program, not just a gimmick or empty
stment pays handsome dividends.

How to Get Started

The cost of computing power is decreasing and special purpose mini-computers are usually
very efficient in doing the tasks the were designed to perform. If schools are willing to
cooperate with a nearby coMege or university and all hav*3 some funds to commit to the program,
then the only missing ingredient to a successful beginning is the faculty member(s) to put it
all together.

The key factor in keepin j the costs really low is that in a time-sharing environment one
teletype can be used four days off-line preparing paper tapes for one day on-line, and this
proposition seems to be a rather good one. Using this approach, five school can share a single
port and all make a significant beginning. If commercial vendors would permit this sharing of a
port, then the operation and maintenance of the system could be left to them. But normally, they
provide more computing power than is really necessary, e.g. a choice of languages, and do not
permit such sharing.

What will cut the cost further is to have enough schools in a pool to support a small-sized
computer which was designed specifically for time-sharing in a single, simple yet powerful
language. The system in use at the University of Louisville is the Hewlett-Packard 200w~A with
16-terminal capacity and a very adequate, extended BASIC. Such a system is essentially a turn-
key operation with a very minimum of operator intervention, and although it is aot now the
newest thing on the market, it is very satisfactory and reliable.

Taking such a system as an example, the monthly lease- pur cha se charge
ports are priced between $500 and $600 per month, a minimum subscription of
four ports can pay for the system to support those ports. The cost per schoc
with five schools sharing each port could then be between $100 and $120
computer becomes available, rates can be established for users within the university to insure
adequate support for the system, so that it can be expanded if that should be necessary, or
fully supported by the university if the funds from the schools grew to the point where they
could support their own systems.

What is outlined here is a way in which cooperation between various institutions can make
possible at a modest cost to all, a beginning which none could afford independently. Even this
suggestion must be adapted to fit any specific situation, and the follow-up years would probably
show even more variation. I will be prepared to present further specific details at the

is u

nder $2

,000

. If

t he

equiva

le n t

1 for

compu t

ing

time

per

month.

the

un ive

rsity t

o in

sure

ERIC

l£l

180

conference to indicate actual costs related to our situation, if there is interest in this
inf ornation.

In developing this progran, extensive use was Bade of the experience gained and aaterials
developed by the three-year Dartmouth Secondary School Project (NS T Grant GW-2246). The aajor
difference in detail lies in the preparation of prograas on paper tape which peraits the
reduction of on-line tine fron 20 ninute blocks to 5-10 ninute blocks for each student. This
certainly encourages the efficient use of conputer tine without losing the "hands-on” experience
in running prograas. It also gives the student a pernanent copy of his progran on paper tape
which can be used again on any terninal having access to the sane language conpiler. TIBS, in
St. Paul, has als. used an optical narked card reader to increase throughput froa their
teletype terninals. The chief advantage here is that the student tan prepare his card deck
anywhere vita only a pencil and a deck of cards. We are also experinent ing with this device.

Explicit nention has not been aade of the denands on the teachers who becone involved in
the use of the conputer in the schools. As an extreae exanple, the on-line day at one school
tends to start at 7:15 a. a. and end sonevhere around 9:00 p.n., with a group of parents wanting
to have instruction after that. You can inagine all the questions this generates for the off-
line days! Tet the teacher aost involved at this school will give all she can to her students,
who are learning like they have never learned before. There are nany fine, dedicated, and
talented teachers in our schools. We can and should seek then out and prepare then, along with
new teachers, for an extrenely deaandiig yet rewarding adventure, the use of the conputer in
teaching secondary school nathenatics.

Conclusion

181

COMPUTER-MANAGED INSTRUCTION:

A BEGINNING AND, A REALITY AT
WESTERN WASHINGTON STATE COLLEGE

Raymond F. Latta and Joan Straughan
Western Washington State College
Bellingham, Washington 9H225
Telephone: (206) 676-3J60

Introduction

The purpose of th.is paper is to discuss the use of the computer in undergraduate education
within the Department of Education, Before beginning, however, we would like to make a
distinction between two uses of the computer in education. Computer Managed Instruction (CMI)
makes use ot batch processing or remote terminals (on a time-sharing basis) to monitor and
manage student progress through frequent testing and analysis related to specific objectives.
Computer Assisted Instruction (CAI), on the other hand, is geared to an interactive terminal
system only, in providing instructional sequences with specific objectives for students.
Methods ot instruction might be tutorial or socratic, drill and pLactice, simulation and gaming,
or problem-solving and information retrieval.

The particular use of the com pu ter pursued by the Department of Education at Western
Washington State College, and described herein, tends to focus more on CMI than CAI. The
rationale for tnis emphasis in the course unit being described is simply one ot logic and
expense. To be more specific: (1) CMI is not as costly as CAI. The hardware and software
costs related to CAI tend to be higher than those related to CMI. (2) Recent emphasis on
individualized instruction has necessitated that educators develop technology to assist in
management and information handling. (3) CMI is less time consuming on the part of the
innovator and requires less expertise, in the initial stages, than does CAI. Preparation,
formative and suramative evaluation of CAI materials often involves a long, tedious schedule.
(4) This college has seven teacher education programs which are competency based, and new
management systems are needed to maintain them.

The course which utilizes the computer withia its curriculum tor both presentation and
course management is Education 444: Instructional Management Systems. The course, which is
worth three credit hours, was developed and tested by the authors of this paper during the
spring and summer quarters of 1971. In all, thirty-two students, mostly seniors, have
participated in the course development and testing.

Course Content, Student Activities, and Scheduling. At first glance, Ed 444 appears to be
simply a survey course dealing with manual and automated instructional systems. The strength of
this course, however, evolves from the required reading, on-site visits, or working through CAI
programs unrelated to the course at hand. Rather, CAI is utilized to present some of the course
material, and CMI, to manage student progress through a unit of the course on a systems approach
to the development of instructional materials. Students then apply the process to the
construction of a small learning package/module.

The schedule for actual course content and related activities (summer quarter) is shown in
Figure 1. This schedule is similar to the one used for the preceding spring quarter when eight
st dents worked through the first trial run of the course. Emphasis on the spring session was
related more to course development, evaluation of instructional materials utilized with the
course, and sequencing of activities, rather than to evaluation of the course overall. At the
conclusion of spring quarter, learning packages were modified on a priority basis.

As is shown in Figure i, the student in Ed 444 is first given instruction on COURSEWRITER
III Author Language, then given instruction in the development of learning packages, and finally
is presented with a survey of nationally recognized individualized instructional systems.
Figure 1 shows each ot these units with the mode of instructional presentation used, student
activities, and student products releated to each unit.

As was mentioned earlier, the course tends to emphasize or focus more on CMI than on CAI.
In view of this approach, it is essential to emphasize CMI through student activities and class
discuss ion.

As illustrated in Figure II, learning packages and the computer are utilized within tne
instructional process for teaching the second unit. The learning packages relate to the steps
in the model of the systems approach taught in this unit. The steps in the model are: problem
identification; tasx analysis; entry behavior/readiness; performance summative evaluation; and
implementation of mon i tor ing[ 1 ]. The packages utilize a presentation format similar to th^t
which the students are expected to follow in the development of their own packages. The primary

* t

In Class
Activities

Intro-
duction
(1 hr.)

:w III
( 3 hrs . )

CW III
(2 l»rs.)

Learning
Packages
(4 hrs.)

* • III
(3 hrs . )

Learning
Packages
(2 hrs.)

Learning
Packages
(1 hr.)

Activity Computer

Activities

Outside of
Class

Program*

cal

(1-2 hrs.
s tudent
time)

Practice
Authoring
CW III
(variable
time)

Program*
System
(1-2 hrs.
student
time)

Computer
Use (CAI
or CMI)

CAI

CMI

Learning
Packages
(4 hrs.)

Programs1
add and
c ilc
U/2 hr.
student
time)

ipi2

PLAN3

IGE4

System

Duluth,

Minn.

System

CAI

Nationally Known Individualized
Instructional Systems

Florida
State Univ.
System

REFLECT5

System

Students author the test questions
in their learning package for use
in a mini CMI system (variable time)

CMI

3 4

TIME (Weeks)

Programs (software) are discussed later in this paper under the gection headed software.
^IPI (Individually Prescribed Instruction)

^ PLAN (Program for Learning in Accordance with Needs)

^IGE (Individually Guided Education)

^REFLECT (Research into the Feasibility of Learnings Emplov ing Computer Technology)

FIGURE 1. Course Content and Schedule for Computer- Re la ted Activities for Ed 44 4, Summer, 1971

1S4

184

difference between the packages used in the course and those developed by the students is that
the test guest ions relating to the specific objectives in the course packages have been
programmed into the CPI I system.

The student, in working through this section of the course: (1) works through the first
package; (2) when finished with t \c learning package and feeling that he has mastered each
objective, he proceeds to thr terminal room; (3) he signs on and receives the criterion-
referenced test for the particular package; and (4) -pon completion of the test, he follows the
directions provided by the CHT system, (The student usually proceeds to the next package and
follows the above sequence of steps until he has finished this section of Ed 444.) It is this
system which provides the student with base knowledge of a systems approach to be followed in
the construction ot learning packages. The instruction is managed by the WWSC IBH 360/Hodel 40
computer through on-line use of the terminal systems, and constitutes a working application of a
semi-CHI system. Concurrent with and following execution of the C(1I sequence, the student, in a
labo rator y- worksaop setting, applies these skills to the actual construction of his or her own
learning package. The subject matter and details of the learning package are left entirely up
to each student.

The synthesis activity for Ed 444. as shown in Figure II, involves the threading together
of those skills learned in the course. The activity referred to is the application and
utilization of CW III, systems theory, student-developed learning package, and insight gained
from exposure to other instructional management systems to construct a student-designed raini-CMI
system (in a very ’inpolished form).

The computer software used for illustrative purposes in Ed 444 would fall short
of being described as very good examples of either CAI or CHI programs, nor are any claims of
excellence made to the students. If a detailed description of computer software used tor
illustration of CAI and CHI were to be provided, it would be lacking in superlatives. Ho claims
of excellence were made to the students. Although the shortcomings were not purposefully
inserted, they contributed to the course by giving students the pleasure of being able to
critique the programs in light of their new-found knowledge, and to make suggestions for
improvements. As such, use of CAI and CHI programs which are of perhaps average quality should
not be outlawed and may well add to the student's opportunity for learning. The following is a
list and brief description of the software utilized in Ed 444}:

1- cai This program using a tutorial mode, teaches the student uses cf many

fundamental op codes in C OURS EWRITER III. The culminating activity of
this short program, which takes from one to two hours to complete, is a
very brief s tu dent- wr i tten course.

2. calc This short program also utilizes a tutorial mode. The program, which

teaches the student hdw to use the computer as a desk calculator, takes
fifteen to twenty minutes to complete.

add This course, which takes from five to ten minutes to complete, teaches a

very short segment of first grade arithmetic utilizing the tutorial mode.

4. syrtem As has been explained in the preceding pages, this unit contains the

ent er ion-referenced tests for each of the steps involved in applying a
systems approach to the development of instructional materials. It
requires c pproxima t el y one and one-half hours on-line terminal time.

The terminal laboratory at WWSC. All CAI and CHI on-line activities take place in VWSC's
terminal laboratory. it is here that eight iBfi 2741 typewriter terminals are located for
student use (Figure III). The IBH 360/Hodel 40 computer at WWSC, with the core allocated to the
terminal system, can support twenty-two terminals. Terminals beyond eight in number are usually
located in individual departments. During the pilot study in the summer of 1971, the terminal
system was available only two hours daily, Honday throujh Friday. The number of terminals and
availability of the system led to some major frustrations.

Findings. Education 444r summer quarter, 1971, was evaluated both formally and informally.
The formal evaluation was undertaken by the Testing Center at WWSC, and the informal evaluation,
by the authors.

The formal evaluation by the Testing Center found the course to be about average in
comparison vith other courses on campus. Several factors were critical: (1) At the beginning

of the course, twenty-one terminals were available to the twenty-four students enrolled. This
number was cut to eight halfway through the quarter as the result of a College financial crisis;
and (2) the terminal system was available only two hours daily, five days per week. The reader
must surely be aware of the ramifications of limited terminal availability both in regard to
course evaluation and the scheduling of students on terminals. The cutback on terminals also

ERLC

195

185

UNIT

MODE OF INSTRUCTIONAL
PRESENTATION UTILIZED

STUDENT ACTIVITIES

STUDENT PRODUCT

1. COURSEWRITER III

1. Textbook materials

2. Lecture

3. Computer (CAI)

1. Practice Exer-
cises (Textual —
off-line)

2. Practice Exer-
cises (on-line)

3. Work through
software package
labelled cai

Completed exercises
and evidence of
completion of
program, cai

2. A Systems .pproach
to the Develop-
ment of Instruc-
tional Materials/
Learning Packages

1. Computer (CMI)

2. Learning Packages
(off-line)

3. Lecture

See paper for expansion of
this section of figure

3. Survey of Indivi-
dualized Instruc-
tional Management
Systems

1. Films

2. Lecture

3. Computer (CAI)

4. Textual materials

1. Examination of
resources ,
philosophy, and
materials re-
lated to each
system

2. To compare and
contrast two or
more systems or
critique any one
system

Short paper

SYNTHESIS: Utilizing CW III, the student developed learning package and knowledge of successful

instructional management systems; the student, using the test questions in his
learning package, develops a mini-CMI system.

FIGURE 2 .

FIGURE 3. A student at work in WWSC*s terminal labo atory. There are eight IBM 2741 typewriter
terminals located in this room with each terminal separated by a semi-partition.

dl i

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1S6

186

increased the student dissatisfaction with the "up"-time on a terminal system which was being
shared (sometimes with Keen competition) by users from other disciplines. Happily, at this
writing, terminals are available to users at WWSC thirty-five hours per week.

Student consciousness and concern resulting from the above two constraints is evident in
iheir comment^ registered on the Testing Center's evaluation. The following are some actual
student comments which have not been edited in any way:

A. 11 1* Work load is too demanding for three credit hours. 2. How can you justify,

educationally, twenty-four students with eight terminals which are available only

two hours daily? 3. More time should be spent on programming the computer. 4.
Course has a great deal of potential."

B. "There should be more access to terminals and credit awarded for this course."

c. "I showed up several times last week and could not }et a terminal. That wasted my
time, and I could not finish my assignments. What is the instructor going to do
about this?"

D. "You talk about individualized instruction. Computers should be available when they
are needed. Speaking for myself, I had difficulty getting on the terminals because I
had other classes during terminal time."

Cited above are just a few comments which resulted from the formal evaluation. Individuals
at colleges considering CAI and/or CM I for utilization in course instruction are probably asking
themselves, "How could anyone let this happen?" The point is that we did not "let" it happen.
Suddenly there we were, afloat without a paddle; but we did manage to survive! The following
are some student comments, in addition to those above, which support our claim to survival:

A i "This course was not only excellent, but it provided me with an opportunity to apply
much of the theory learned in other courses to a learning problem. When I began this
course, I had both fears and misgivings about the computer. These no longer exist,
and I feel that you opened up a new field for me. Do you know of any schools where
tney have a computer?"

3. "I would like very much to do some further work in this area. Is there going to be a
course we can go beyond this course?"

C. "I enjoyed the course a great deal. I learned a tremendous amount for a short period
of time. I came completely ignorant of computers, and I feel I have left with
something. I particularly appreciated the fact that the instructor worked hard and
practiced what he preached.”

Informal evaluation, which was undertaken after the formal evaluation, was carried out by
having a random sample of the students, twelve in all, respond to the following question:
"Putting aside the fact that you suffered due to (1) availability of terminals and (2) the
difficulty of scheduling your time to the two hours which the terminals were available, how
would you rate this course?" These students were given a rating scale of 0=poor; 1=fair;
2=average; 3=good; 4=excellent. The results: Five students rated the course excellent; four

students rated the course good; two rated the course average; and one rated the course fair.
Most of the subjective comments were similar to those which were offered to substantiate the
successfulness of the course.

While d^ta gained from either of the evaluations offers no statistical impact, it did
provide the course authors with feedback related to the successfulness of the cour .e which could
be utilized in future planning.

Future Plans* Given that both enrollment at the College remains at its present level and
that Ed 444 Decodes part of an actual program, the following changes and updating will occur:
(1) Learning packages will be revised using feedback from students during the summer pilot
study. Student comments throughout the course were very strongly in favor of the utilization ot
learning packages to present course material. Students felt that this use not only provided
them with an observable application but also with a model after which to pattern their own
packages. (2) The program "system" will be revised to increase reinforcement and provide more
information to the student about his score. The rationale for further developing this program
is similar to that provided for further development of learning packages to be utilized in the
course. {3) A progress/summary table will be provided for the instructors of Ed 444 showing the
time spent, score on each cr iter ion- ref erenced test, etc., tor each student. Changes in
computer software are now possible because of a new programming language developed at WWSC which
permits course authors to use COURSEWRITER III syntax in combination with an interactive
problem-solving language (WPL) . WPL (Western Programming Language) is a subset ot PL/1 which
was designed to run in an 88K partition of an IBM 360/Model 40. (4) The actual teaching of CW

III will be dropped from Ed 444 in order to lighten the load of the course. Students will take
the program "cai" and may, working with the course instructors, independently pursue "hands-on"
projects.

fl££°§®llDda t ion and Summary. Based On our experience with using the computer in
undergraduate curricula in the Department ot Education at WWSC, we would like to otter the
following recommenda ti ons or suggestions to those considering a similar application: ( 1) Get
the support of the Education Department. It is important that the Department make a coimitient
and recognize that the planning and development of such innovative practices is 1 1 me- consu ling .
For example, if one is adding a three-credit hour course of this nature to a nodal teaching
load, a half-time staff assignment for the course would not be liberal by any leans. (2)
Establish the course as part of a program leading to a degree or certification. Do not develop
it as an elective unless student and faculty interest is such that an adequate number it
students can be solicitied to offer the course at least twice a year. To put this amount ot
work into a course and have is shelved would be a shame. (3) Assure the availability of
terminals so that students can exercise freedom to use the computer when they have time. This
is one of the basic advantages to CAI learning, and particularly the first encounter ot a
student with the computer should be an enjoyable one. (4) With the projected growth of

computers in this country, 125,000 additional computers by 1980[2], utilization of the computer
in undergraduate education is a must. The utilization of the computer in classroom instruction
in K-12 education in this country has increased such that departments of education at
institutions of higher Learning are shirking their responsibilities if they do not expose future
teachers to the computer as a medium for instructional coamun ica t ion[ 3 ]. (5) Hather than

consider a course which involves students* learning and applying a programming language,
consider utilizing the computer as a medium within the course presentation. The latter
introduces the student to the computer in the ultimate, for he is provided the opportunity to
see an instructor's actually making use of the computer. It has been said that "one does as
others do" and that teachers teach using the methods by which they were taught. If one is to
accept this premise, then the above application may be more important than actual courses which
teach CAI.

In summary, we would like to suggest that education departments in colleges throughout this
country consider carefully v he use outlined in Recommendation 5. It is here that we suggest
utilization of the computtj in undergraduate curricula in the department of education begin.
Gaining experience and success from this initial application will make the nex** step, courses in
CAI and CMI, an easy transition. Educition 444 was successful and has proved worth pursuing.
The authors of this paper view the frank appraisal of experiences discussed throughout this
document as a ;eans of moving forward.

REFERENCES

1. Latta, Raymond F., and Papay, James, "Planning for Change: An Iterative Approach", Planning

and Changing: A Journal for School Administrators. Number 2, July, 1971, pp. 70-80.

2. "Will We Call Them the Sensitive Seventies?", Administrative Management. January, 197 , p.

22.

3. Dick, Walter; Latta, Raymond F. ; and Rivers, Leroy, "Public School Activities and Related
Sources of Information Concerning CAI in United Stated", Educational Technology. Number 3,
March, 1970, pp. 36-39.

A com BISON or TYPES of feedback to
STUDENT BESPOMSES IN A CAI UNIT

Harold L. Schoen
Virginia Polytechnic Institute
and State University
Blacksburg, Virginia 24Q61
Telephone: (703) 951-2471

Introduction

There is nuch resistance in education to the use of tutorial computer assisted instruction
in the classroom. The nain ob^ .tions seen to be:

a* it costs too much, aud

b. it is not an inprovenent over existing
nodes of instruction.

At present, both objections appear to be valid. However, the first is probably a tenporary
condition. As schools purchase nore conputer tine for nanagenent and problen solving uses, the
on-line cost nay well become an insignificant factor. At any rate, this paper is directed to the
second objection.

The question of how individualization of instruction via CAI can best be achieved is "an
alnost untouched problem** (Gentile, 1967). This study is an attenpt at "touching" that problen.
Four instructional treataents which differed in the degree of individualization and
personalization (references to the student by nane) in a CAI progran designed to teach the
mathematical concept of function were written. Mean achievement and attitude scores of groups of
students receiving the different treataents were then conpared.

Background

Little research or developnent in CAI had occurred prior to 1964 (Dick, 1965; Suppes,
1966). One study conducted at I.B.R., which compared achievement scores of students learning a
topic via three nodes of instruction, CAI, a standard classroon approach, and progranned
instruction, showed results which strongly favored the CAI treatnent. However, the Hawthorne
effect of novelty was probably great (Dick, 1965).

In another early study two groups of high school students received instruction in logic
fron a conputer. One group received a fixed seguence of itens while subjects in the other were
branched depending on their perforaance during the lesson. The posttest ach.evenent scores were
significantly higher (.05 level) for the branching group tha^ for the fixed sequence group
(Coulson, 1 962) •

Soae trends which early research and developnent in CAI seemed to indicate were that:

a. the type of error a student nake nust be
indicated to bin,

b. the CAI prograa nust provide help to
correct student errors, and

c. this help should be given inneuiately
following the error (Dick, 1965).

Probleas which became apparent in early CAI developnent were:

a. developnent and evaluation of better
teaching strategies to utilize the capabilities
were needed, and

b. prograns designed to record student responses
and present then for analysis in rapid and
intelligent fashion were not available (Filep, 1967).

The second of these problens has been virtually solved as was exenplified in the data collection
for this study.

ERIC

189

1S9

CAI research a$d development in the last four or five years has been such sore extensive
than previously. The recent research studies which are cited have been restricted to those
attempting to isprove CA1 teaching strategies since that is the sain thrust of this
invest igat ion.

It was found in a study utilizing a four hour CAI course in probles solving that
achievement scores were affected by certain personality traits coupled with the type of CAI
treatment. one group of subjects took the computer course imdividually at the terminal while
subjects in another group took it with a partner. The subjects who tended to have dominant
personalities achieved more (as measured by the posttest) if they worked alone. Those who tended
to fear tests achieved more with a partner. Several other personality traits were considered
with no significant differences in test scores (Sutter, 1967). Further findings tend to support
these results (O'Neill, 1969; Ha jer, 1970; Gallager, 1970).

No significant differences in learning or retention were fomnd among groups receiving five
different types of feedback on a CAI unit which taught science concepts to university
upperclassmen (Gilman, 1967; Gilman, 1969). Significant differences were not found in
achievement scores in another study comparing three modes of instruction - two modes of CAI and
one conventional classroom mode (Proctor, 1969). The relative effect of verbal definitions and
numerical examples as corrective feedback in a computer assisted learning task was investigated
by Keats and Hansen (1970). Results favoted the use of verbal definitions.

Several studies were located which tend to signf iica ntl y favor the use of CAI for various
instructional tasks. These include CAI over programmed instruction (Dick and Lalta, 1970) , the
value of CAI for testing students (Fergu~on, 1969), CAI over the traditional classroom
instruction (Stro jkie wicz, 1968), and the value of CAI to teach geometric topics (Dennis, I960).
In another study, however, two nodes of CAI were compared - one consisting of multiple choice
questions and the other of a series of lecture-like presentations - with no significant
achievement differences resulting (Bauldree, I960).

Grayson (1970) summarizes the state of the art in CAI research,

While many (CAI) studies have been conducted in many of then, the
Hawthorne effect of novelty may be the overwhelming factor.

This problem notwithstanding the research does seem to show that CAI has potential as a node of
instruction, and that the individual student must be studied in an attempt to meet his needs.
However, no clearly superior approaches to CAI development appear to be emerging.

Method

Two CAI units were developed by the researcher —Unit A, including concepts prerequisite to
functions such as sets, ordered pairs, and graphs; and Unit B, containing the definition of
function, graphs of functions, and functional notation. Unit A and Unit B were written in I.B.H.
Coursewriter III, version 2, and are available on one of The Ohio State University's I.B.H.
360/50 computer systems. Four types of feedback to incorrect student responses were written in
Unit B. These are the result of crossing two levels or each of two variables, I
(individualization) and P (personalization).

The levels of I were defined as follows.

I* - the student receives feedback following an incorrect

response which states why his answer is incorrect and
gives the correct response.

I" - the student receives feedback following an incorrect

response which states that the given answer is incorrect
and gives the correct answer with a reason why it is
correct, but the feedback does not refer specifically
to the student's response.

The feedback to correct student responses was the sane for the two levels of I. The lengths of
the feedback statements for the two levels were as nearly equal as possible.

The levels of P were defined as follows.

P* - the student's first name appears in some of the feedback

to both correct and incorrect responses. The frequency of
use of the first nane was decided by what seemed reasonable
to the researcher. The only pattern followed for use of the
first nane was that if the name was used in feedback to one

2&°

response to a question It appeared in feed back to any response
to that question* H'ice, the student's error nate did not affect
the frequency with naich his first n*ae appeared. To be exact*
the naee appeared in feedback to responses to 41 of 56 questions in
Osit B.

the student's naee never appeared in the feedback

The four types of feedback then sere I'P', I'P", I"P', and I"P" which result froe crossing the
tvo levels of I with the tvo levels of P.

An an exanple of the type of feedback for ea-h group, suppose this question is asked the
subject.

So ie the previous question, S * [(x,y):y * 2x ♦ 3 and x * 1, 2, or 3] is a function.

If the student response is c then the I'P* feedback is:

x is only the syabol representing the values in the doaain and y, those in the range.
The correct ansver is b, Edgar.

The I'P* feedback is the saae except 'Edgar* is oaitted.

The I"P# feedback is:

The I"P" feedback is identical except 'Edgar' is ositted. feedback for the tvo I” groups is the
saae for any incorrect response; that is, c, a, or d.

The CAI units vere based on a set of researcher developed behavioral objectives which
followed the recoaaendations of several authors (Bohein, 1960; Gagne, 1964; Gagne and others,
1965; Arathvohl, 1964; Lindvall, 1964; Hager, 1962; Tyler, 1964; Ullaer, 1967). The branched
programed CAI units vere designed to lead the students to achieve the behavioral objectives.
Three achievement tests, Q, F, and S, and an attitude scale, T, vere developed (twenty items of
the thirty-iten attitude scale vere used with permission of Carlton Bobardey, Hichigan State
University). Two pilot studies for purposes of revising and refining the instructional units and
evaluation inntrunents preceded the final study. Q was a tvdnty-item test of Unit A, R was a
fifteen-item test of Unit B, subunit 1 (the definition of function), and S was a fifteen-item
test of Unit B, subunit 2 (functional notation). Q, B, and S vere composed of multiple choice
items. The number of items and the material tested by each instrument were decided based upon
pilot data.

Sixty pre-calculus mathematics students at Ohio State University in the Vinter Quarter,
1971, vere the subjects. They comprised tvo sections of Hath 150 (students are placed into
sections at Ohio State from a shuffled deck of class cards). The subjects vere then placed
randomly in equal nuabers into the four treatment cells. During the first three weeks of the
quarter all subjects were administered Unit A followed imaediately by Test Q, then Unit B,
subunit 1, followed immediately by Test E, and finally Unit B, subunit 2, followed immediately
by Test S, all via an I.B.fl. 2741 terminal. Tvo days after all subjects had received the
computer treatment* they r^jpleted T, the attitude scale, using pencil and paper. The Unit A
treatment was included prior to the experimental unit on which the comparisons vere made (Unit
B) in order to decrease the Hawthorne Effect of novelty. The Unit A treatment was identical for
all four treatment cells.

The null hypotheses of no differences between mean scores of the combined group I'P9 and
I'P" compared with the combined group I”P' and I"P” and of no differences between mean scores of
the combined group I'P* and I"P# compared with the combined group I'P" and I"P" on each of the
criterion measures B, S, and T vere posed. Nearly equal cell means prompted eliminating the use
of Test Q scores as a covariate. Thus the hypotheses were tested using two-way analyses of
variance with B, S, and T scores as the respective dependent variables. The BHD05V program for
testing general linear hypotheses was used.

a. whose domain is [9, 7, 5} and whose range is (1, 2, 3]

b. whose domain is [ 1, 2, 3] and whose range is [9, 7, 5]

c. whose domain is x and whose range is y = 2x ♦ 3

d. none of the above

No, the doaain is the set of values x (or the first coordinate) nay take, so the
domain is [1, 2, 3]. The range is the set of y values so y = 2x ♦ 3 has values 2(1) ♦
3 * 5, 2(2) ♦3*7, and 2(3) ♦ 3 * 9. The correct ansver is b, Edgar.

191

Results

The results of the nain comparisons are summarized Id the following table.

Usisg fi scores as the dependent variable the I effect is clearly non-si gnif leant, but the P
effect is significant with p less than .11. With the ssall II in each cell, this say be ar.
indication of none differences in the levels of P; nanely, that the P 9 groups, those receiving
feedback with student baits included, tended to perforn better than the P" group on H.

The tSBults of the analysis of variance using S scores as tho dependent variable indicate
that students receiving the I" treatnent scored higher (p less than .04) • This is in contrast to
nearly equal leans on Test B for the two groups. Analyzing the P effect shows that the P* group,
those receiving their uaaes in feedback, scored higher than the P” group, though not
significantly higher. The reliability of the fifteen-iten Test B was estimated by KB - 20 * .70
(M » 60) .

To analyze the T (attitude) scores, student responses were coded fron 0 to 4 with a higher
score indicating a noce positive attitude. The results in the Table are based on student scores
conputed by taking the sun of the coded student response for each of the thirty itens. Using
correct to nean a 3 or 4 on an iten and incorrect to neao a 0, 1, or 2, the reliability of this
thirty-item instrument was estimated by KB - 20 a .84, where H = 58. Here M is 58 instead of 60
because two subjects dropped the course before the administration of T. The attitude scores of
studeats receiving the P9 treatnent are higher than those receiving the p" treatnent at the .07
probability level, while the I effect is clearly non-significant.

Further analysis showed non-significant correlations between attitude and achievement and
snail positive correlations between Unit B tine and attitude scores. Mean student CAI treatnent
tine was 171.07 minutes. This includes the tine taken to complete Unit A and Unit B as well as
tests Q, B, and S. Student tine did not differ significantly anong the treatnent cells.

Conclusions

Tie results of this study do not suggest that the type of individualized feedback
(I1) written for this progran yields better student achievenent or attitudes scores than non-
individualized feedback (I"). In fact, on one achievenent test, scores were significantly higher
in the I1 group, while no significant differences in the levels of I were found in the other
achievenent test scores or the attitude scores. T«ese results, at first glance, seen to imply
that a statement of the correct answer with a reason why it is right is better corrective
feedback than an individualized explanation.

A closer look at the individualization levels, however, suggests that subjects in the I •
group were not ready to continue to the next frane following their corrective feedback while
those in the I" group were. An incorrect answer to a question, certainly in nost cases, implied
that the subject did *ot understand the concept treated in that question. The I9 feedback
explained the fallacy in the incorrect answer and stated the correct answer. Thee the student
went to the next frane even though no reason for the correct answer was given. On .he other

hand, the erroneous student who received the I" feedback was given an explanation concerning the

correct response. The explanation of the correct answer was probably the key difference in the I
levels of feedback.

The use of a student's first nane in the CAI progran seemed not only pleasing to him
(attitude difference at p less than .07), but there was also some evidence that better
achievenent occurred when the first nane was used. The positive correlation between Unit B tine
and attitude scores seems to indicate that the students who enjoyed the progran nost did not
hurry to finish, while those who disliked it rushed through. This result aay have been caused by

a few students who became frustrated because they did not understand the explanations or were

sinply tired.

In sunnary, the results of this study seen to imply that:

a. an important conponent of corrective feedback is an explanation of the concept
in question if that explanation innediately precedes a new frane,

b- the attitude of students toward a CAI tutorial progran is improved by use of
their names in the progran, and

c. there is a direct relationship between student on-line tine and attitude toward
a CAI progran (provided that the progran is designed so that a student error
rate does not greatly affect his progress through the unit) .

192

Any conclusion concerning the desirability of indi f idualized corrective feedback does not seen
virrutid. flora research ia seeded to aaanar thia important g. nation.

Future Research

Soaa research related to the quest* on of hoe to individualise CAI tutorial progran* is
presently beiag planned. k graduate student at The Ohio State University, Kenneth Taylor, has
proposed a study vhich vill replicate the design of thia one, vith a different CAI progran and a
different aanple population. His progran vill be designed to teach geonetric concepts to college

seniors.

k holloa- up of this stuay in vhich nore feedback treatnents are considered is nov being
designed by the investigator, k conbination of the I* and I* feedback is planned, adding a third
level to the individualisation variable. It is hoped that this study can be done vith a aanple
of high school juniors or seniors since the results could then be generalized to a larger
population than those of the reported study.

EBPEBEMCES

Bauldree, A. I. Individual and group differences in learning under tvo different nodes of
conputer-assisted instruction. (Doctoral Dissertation, Florida State University)
Dissertation Abstracts. 1968, 2 9, 1443-A. (Abstract)

Bohein, J. Inplications of the individualization of instruction for curriculun and instructional
design. Audiovisual fgstrugtlon. 1968, 68, 13, 238-242.

Coulson, J. I., Bstavan, D. P«, flelargno, I. J., and Silbernan, H. F. Effects of branching on a
conputer controlled uutoinstr uctional device. Journal of Applied Psychology. 1962, 46, 389-
392.

Dennis, J. I. Teaching selected geonetry topics via a conputer systen. (Doctoral Dissertation,
University of Illinois) pisgeejation Abstracts. 1968, 29, 2145-A. (Abstract)

Drck, H. , and Lalta, B. Conparative effects of ability and presentation node in conputer*
assisted instruction and progranned instruction. ££ Connmication levies. 1970, 18, 33-37.

Dick, H. The developnent and current status of conputer- based instruction. Aserlcsn Educational
Besearch Journal. 1965, 2, 41-54.

Ferguson, B. L. The developnent, implementation, and evaluation of a conputer-assisted
branched test for a progran of individually prescribed instruction. (Doctoral Dissertation,
University of Pittsburgh) Djsserta^jog Abstracts. 1970, 3856-A. (Abstract)

Pilep, B. T. Individualized instruction and the conputer potential for nnss education. |V
CQSsunlcaUos Ievlev, 1967, 15(1), 102-113.

Gagne, B. fl. The inplications of instructional objectives for learning. In C. £• Lindvall (Ed.)
Defining Educational Oblec^jvef. Pittsburgh, Pa.: University of Pittsburgh Press, 1964.

Gagne, B. fl. and others. Psychological principles ip sisten develppaeat. Bev York: Holt,
Binehart and Hiaston, Inc., 1965.

Gallagher, P. D« An investigation of the relationship of learning characteristics and success in
a conputer nnnnged instruction course for graduate students. Paper presented at the neeting
of the Anericnn Educational Besearcu Association, April, 1970.

Gentile, J. I. The first generation of CAI systens — an evaluative reviev. pv Conaiinicatlop
lliill, 1967, 15(1), 23-54.

Gilaan, D. A. feedback, proaptiag, and overt correction procedures in non-branching conputer
assisted instruction progran*. ^ourgal gf iesf jCCfc. 1967, 60, 423-429.

Gilman, D. A. Coaparisons of several feedback aethods for correcting errors by conputer-assisted
instruction. Journal 2t Educational Psychology. 1969, 60, 503-508.

Grayson, i* P. A paradox: the pronises and pitfalls of CAI. EDUCQfl. flarch, 1970, 1-3.

203

193

Keats, J- G. , and Hansen, D. i. Definitions and QXunplen ns feedback in a CAI stimulus-centered
■athesatics program. Unpublished manuscript, Florida State University, 1970.

Krathvohl, D. R. The taxonomy of educational objectives — Its use in curriculum building. c.
*!• Lindwall (Ed.), Defining gjucatjg^aj Objectives. Pittsburgh, Pa.: University of
Pittsburgh Press, 1964.

Lindvall, C. II. The importance of specific objectives in curriculun development. In C. n.
L'udvall (Ed.), Def iripg educational Objectives. Pittsburgh, Pa.: University of Pittsburgh

Press, 1964.

Hager, R. F Preparing IflSttuciiflnal Objectives. Palo Alto, California: Pearon Publishers,

<962.

najer, K. S. A study of computer-assisted nultinedia instruction augmented by recitation
sessions. (Doctoral Dissertation, Florida State University) Dissertation Abstracts, 1970,
JO, 3641-A. (Abstract)

OfNeill, H. F. Effects of state anxiety and tasks difficulty on con pu ter- assisted learning.
Journal of Educational Psychology. 1969, 60, 343-350.

Proctor, U. L. A comparison of two instructional strategies based on computer-assisted
instruction with a lecture-discussion strategy for presentation of general curriculun
concepts. (Doctoral Dissertation), Fit rida State University) Dissertation Abstracts. 1969,
29, 2075- A. (Abstract)

Stro jkeivicz, L. W. Training for problem-solving skills utilizing a coaputer-assisted
instructional method. (Doctoral Dissertation, University of California at Berkeley)
Dissertation Abstracts, I960, 29, 1498-B. (Abstract)

Suppes, P. The uses of coaputers in education. Scientific American. 1966, 215, 206-220.

Sutter, E. n. Individual differences and social conditions as they affect learning by computer-
assisted instruction. (Doctoral Dissertation, University of Texas) Dissertation Abstractsf
1967, 2 8V 4012-A. (Abstract)

Tyler, £• W. Some persistent questions on the defining of objectives. In C. H. Lindvall (Ed.),
Defining Educational Object jves. Pittsburgh, Pa.: University of Pittsburgh Press, 1964.

Ullaer, E. J. A study in the development of a technology based aodel for instruction design.
(Doctoral Dissertation, University of Wisconsin) Dissertation Abstracts. 1967, 28, 4551-A.,

2C4

194

USING A COHPUTER TO SUPPORT THE TESTING PBOGR&9
III AUDIO-TUTORIAL BIOLOGY

Arthur Vagner and Bonaid Bleed
Joliet Junior College
Joliet, Illinois 60436
Telephone: (815) 729-9020

Intro duction ’ **

In courses of study employing individualized instruction such as the audio-tutorial biology
program at Joliet Junior College, one is faced with the problem of producing multiple versions
of objective tests for each ninicourse in order to naintain the integrity of the testing
program. It is a particular problem because the objective test is necessarily short (10
questions, nulti.-le choice) in order to provide tine during the testing session for the oral
quiz. Studants easily learn tha answers for this short test Iron others who have already taken
it. Subsequent evaluation of this student* s progress then becones quite invalid. The obvious
solution was to aake a different version for each of the 40 testing sessions given for each
ninicourse. All versions of the tost had to be as sinllar as possible wito regard to difficulty
and representation of the subject natter. Forty test versions \ad to be produced for each of
the 15 ninicourses presented io the senester..

It was soon apparent that the production of the tests was beyond the capacity of the
biology departnentis secretarial resources, and the biology staff sought out the data processing
department and the conputer for assistance. Together, they developed an operation which not only
solved the problems at hand but also increased the capabilities for testing beyond earlier
expectations.

Developing the Test

The biology staff wrote 4 questions at the knowledge level of Bloon's taxonony (Bloon,
1956) for each behavioral objective in the ninicourse. These forned a question pool fron which
were drawn individual questions for each version of the test. Two criteria were established for
the selection of questions for each test.

1. Questions for each test were selected on a randon basis.

2. The randon selection was controlled to insure the equal distribution of questions
anong the objectives of the unit.

Producing the Test

After the questions were conpiled for each test, they were produced in nultiples of 8 to
accommodate ou r testing nethods (Postelthwait, 1968). An answer sheet was also produced for each
version of the test in the sane fornat as the question sheet. To the left of each question on
the answer sheet was given the ninicourse nunber, the behavioral objective nunber which each
question was based, and the correct answer. Figure 1 shows one question fron such an answer
sheet •

The answer sheet expedites feedback to the student fron the instructor innediately after
the test is conpieted and graded not only about the question nissed but, nore inportantly, to
the specific behavioral objective upon which it was based. This provides bin with explicit
inf or nation to guide preparation for a retest.

L sing the Conputer

Except for writing the initial test questions for each behavioral objective in every
ninicourse, all of the other operations were conpu terized, including the printing of the
nulti pie copies of each test and its accoapanying answer sheet. The initial step was to
keypunch tie test questions and possible responses. A card fornat was designed to p^rnit any
type of question, objective, short answer or essay, any length of question and any nunber of
responses. Colunns 1-3 were used for question nunber, colunn 4 for line nunber, colunn 5 for
ninicourse nunber, colunn 6 for objective nunber, colunn 7 for answer, and colunns 8-70 for the
text of the question or response.

Substituting, adding, or deleting questions can easily be accommodated by this systea. This
fornat also nade it possible to re-sort the card: If they becane disordered. The cards were
stored in groups by ninicourse which peraittel the easy selection of any ninicourse for test
preparation. For proficiencies or final exans, the entire deck was selected.

195

205

FIGURE 1.

Darwins experiences on the HMS beagle led him to conclude
that

A. Organisms inherently demonstrate variations.

B. Organisms must change when the need arises.

C. Organisms, only which are the fittest, can compete.

D. Organisms, respond mostly to genetic drift rather than
mutations •

Q = minicourse number
□ as behavioral objective number
* = correct answer

A sample question from a typical answer sheet keyed to a minicourse and behavioral
objective.

FIGURE 2. The computer system flow chart.

O'J,

196

FIGURE 3. The computer program flow chart.

*0*

197

The computer systen involves only 1 program vritten in standard COBOL and run on a mall
NCB Century 100 computer. The systen flow chart is shown in Figure 2.

The first step in the coaputer prograa reads the cards for the selected ainicourse and
writes the card records on a dish in the froa of a aaster file. Second, a series of raados
nuabers is generated that equals the nuaber of questions required and evenly distributes the
question aaong the objectives. Third, the aaster file is searched for the questions Batching
the randon nuabers. When a Batch is found, the question froa the aaster file is written to an
extract disk file. This step is repeated until all selected questions have been vritten to the
second file. Fourth, the second disk file is used as input to print out the answer sheet and
finally to print out the required nuaber of question sheets. Upon the conpletion of the test
set for this individual version, the prograa branches back to the second step and repeats the
sane procedures for another version. This is illustrated in Figure 3.

This systen is advantageous for courses which require nultiple versions of nany tests on a
regular basis. The a udio- tutorial and prograaned instruction nethods lend thenselves to this
type of test preparation. It would be quite difficult and expensive to duplicate this without a
coaputerized systen.

Summary

To facilitate the testing prograa for in audio-tutorial systen in the biology departnent, a

method was devised to generate different tests for each of the 40 snail test sessions. Each

test fulfilled the following raquirenents.

1. Each had different, randomly selected questions.

2. Each had an equal distribution of questions aaong the objectives for the unit.

3. Each had the capability of having any nanber of questions.

4. Each had an individual answer sheet with the correct answer marked and the ainicourse
and objectives labeled.

5. Each had the capability of being printed in any nuaber of student copies.

6. Each had to be capable of handling any type of question of any length.

To fulfill these requirements, the biology department looked to a computer. Working with
the data processing center, a snail system was designed, and a coaputer prograa was vritten in
COBOL 'ihich could generate the tests according to the requirements.

REFERENCES

1. Blooff, B. S., Ed., Taxonomy of Educational Objectives, Netf yorfcS David flcKay Company, 1956.

2. Postel thwait , S. N. , Novak, J., Hurray, Jr., H. T., T£e *ud jo-Tutorja j Approach to

Learning, flinneapolis; Burgess Publishing Co., 1969.

198

2C8

INITIAL DEVELOPMENT OF INDIVIDUALIZED
INSTRUCTION WITH COMPUTER SUPPORT

Richard F. Walters, Gail N. Nishimoto
John M. Horowitz, Ray E. Burger
University of California
Davis, California
Telephone: (916) 752-3241

Effective use of computers in the learning process can be achieved only after a great deal
of patient preparation, testing, evaluation and evolution. The road already travelled blurs
rapidly for those whose sights are set on the new horizons opened by achievements already
secured. These visionaries will naturally wish to share their most recent successes and to chart
the road ahead; their guidance is essential. For those who follow in turn, painfully tracing the
fading steps of the pioneers in this field, it often seeas that the gap is too great, the
signposts too few, and the pitfalls too nuaerous ever to attain those plateaus considered old
hat by the experts. This paper is an attempt to add a few signposts to the beginning of the
road, in the hopes that effective computer support of the learning process aay become a major
highway rather than a limited thoroughfare. More specifically, this report describes a series of
simple programs that provide self-evaluation for the student, course review for the instructor,
and an opportunity to proceed into aore sophisticated computer- supported instruction.

Instructional use of computers has developed slowly tor several reasons, including problems
of developing adequate hardware and software support, dollar costs of entry and continuation in
computer support, incomplete understanding of the most appropriate methodologies suitable for
computer technology, the time required for significant educational returns on the initial
preparation of instructional material and a significant lag in the acceptance of computer
approaches to learning. Although all these factors play a role in computer use for instruction,
the problems of operational cost, methodology and short-term returns offer the greatest promise
for creative solutions.

Operational costs of a time-shared system can be allocated to the computational steps
performed, the storage of information in machine-readable form, and data communication. The
additional costs of timesharing can be divided between the coaputation and communication costs
of the system. The major opportunities for realizing savings exist in the use of teaching
strategies that minimize storage of large files. Additionally, the time spent by a student at a
remote terminal dictates the number of terminals, communications lines and entry ports that the
system must provide for a class. Some cost savings can therefore be realized by restricting the
sTudent*s computer time to those experiences offering learning benefit.

The instructor who seeks to use a computer as a teaching aid is confronted with a need not
only to familiarize himself with the unique characteristics of the computer, but also to define
with considerable precision his teaching objectives so as to utilize this auxiliary technology
effectively. It often happens that the computerization of a learning segment is undertaken
without adequate planning, and the results are usually unfortunate. Furthermore, when the
instructor has his objectives well in mind he may not be sufficiently aware of the computer
technology to take full advantage of the versatilities available to him.

A major factor affecting the initiation of computer-related instruction is the time
required for a system to deliver effective learning experiences. A typical first encounter with
computer implementation of a learning sequence would begin with systems problems when the
equipment is first installed, followed by a protracted period of program creation and
implementation, then followed by a still longer time for preliminary testing of the material,
evaluation and modification prior to introduction in a course. Attempts to by-pass this sequence
by acquiring available programmed instruction usually fail to involve the instructor
sufficiently in the de7elopaeat process to educate him to the merits and weaknesses of this
technique.

As a result of the factors described above, persons wishing to introduce computer
technology in the instructional process find themselves on the horns of a dilemma, faced with
tradeoffs between effective instruction, inexpensive implementation and the tine required for
startup. There is no single solution to this problem; however, the technique described below
appears to serve as an effective entry point without major drawbacks in any of the problem areas
cited above.

Historically, the Davis campus of the University of California had done little to implement
on-line computer sup ort prior to 1970. The major step that had been taken was to acquire a
third generation computer system capable of supporting timesharing, an! :o back that system up
with an existing timesharing system during conversion to the new eguipme/t. in addition, some

199

209

attempts to explore instr uctional use of computers bad been initiated, notably vithin the school
of eedicine and the departeent of electrical engineering. Aeieal physiology, on the other hand,
had been exploring the nerits of individualised instruction froe other sethodological
approaches, aimed at increasing the opportunities for independent study and self-evaluation. In
the susaer of 1971, the departsent of anisal physiology and the Office of Hedical Education
decided to attespt a joint developsent progras that vould enhance self-evaluation for both
departnents.

The faculty of the departnent of aninal physiology vere faced vith rapidly increasing
enrollment in an already large undergraduate class in systenic physiology* In order to naintain
instructional guality, these faculty had evolved a teas teaching concept of optional lectures
supplenented by audiovisual natorial containing the sane concepts, by self-tests adninistered
vith a hand-scored see-through board and by snail tutorial sessions. The School of fledicine also
offers teas' taught courses, interdisciplinary in nature, as a part of ita regular core
curriculum. The course connittees for these courses include representatives of the Office of
Hedical Education vho have responsibility for the delivery and evaluation of courses and also
for the developnent of nev teaching nethodologies, including conputer support. Here, too,
students vere anxious to receive increased self-evaluative experiences. The opportunity to
conbine forces appeared favorable, and as a result the tvo schools decided to vork together in
designing a single progras for self-evaluation. Design of the nethodology vas accomplished in
joint sessions; the progran vas introduced sinultaneously in both schools, using slightly
different fornats as described belov.

Description qf Self-Evajualipfl System

The computer supported self-evaluation system provides for the entry of ansvers to problen
sets so that students can reviev these tests by Beans of a computer terninal, receiving
inmediate tutorial guidance vhile their responses are stored in a file available for reviev by
the instructor. Three interactive conputer programs vere vritten to support this process: the
first for entering the ansver key, the second to be used by the student in taking the self-test,
and the third for use by the instructor to evaluate overall student perfornance in a given
course segnent. In addition, the prograns use tvo disk files, one containing student
identification and the second a set of consents directed to individual students.

In entering the ansver key (fig* 1) the instructor (or a teaching assistant) is first asked
to provide a title for the self- test? and then to specify certain procedural options such as the
type of identification required and the decision to provide or vithhold the correct ansver. The
next step is to enter correct ansvers to each question. The progran vas designed to elininate
computer storage of questions for several reasons. Since questions can be easily typed and
duplicated for distribution, keypunching and storage of the questions are unnecessary and
expensive. The tine required for a student to consider individual problems is not productive in
terns of the nan-nachine interaction, and it night be better acconplished avay from the terninal
so as to save on connect costs as veil as freeing the terninal for other students* use. In
contrast, hovever, the ansver options are nore flexible than the aornal multiple choice tests
typical of nost computer-scored experiences: they nay be either numeric or include conbinations
of alphanuneric characters. Huneric ansvers are considered correct if they fall vithin a
specified range of the "correct” response. Typically, an instructor will use a nixture of
numeric, true/false, single vord and multiple choice responses in a given test.

Polloving entry of the ansvers, the instructor then enters feedback responses for incorrect
ansvers. These responses nay direct the student to specific reference material, contain
suggestions for reviev or instruct the student to contact a tutor for clarification. The
responses nay be recalled on the basis of a single incorrect ansver or a combination of errors,
depending on the instructors judgement.

At the conclusion of the instructor* s session, there vill be stored on disk a series of
ansvers, tutorial consents for the conbinations of incorrect ansvers, and a separate file of
personal consents for students. At this point the problen set is ready for the second step,
during vhich the student enters his ansvers. Prior to his arrival at the terninal, each student
vill have received a problen set vhich he is instructed to revxev on his ovn before talking it
over vith the conputer. He is usually encouraged to use those auxiliary aids appropriate for the
course segnent and to delay his session at the terninal until he is reasonably satisfied that he
understands each question. When he signs on, giving his nane and/or his code nunber, any
consents stored under his nane vill be displayed before he enters his ansvers. The progran then
requests the ansvers to the problen set, giving the student an opportunity to reviev and correct
typographical or other errors before they are scored (fir. 2). When the student indicates that
he is. satisfied vith his ansvers, his performance is evaluated. He is given his overall score,
inforned as to vhich questions he nissed, and then provided the tutorial infornation appropriate
to his incorrect responses. He is then free to leave the terninal. Usually a student vill
require five niautes or less for a set of tventy to thirty questions.

200

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-BOJ- OGETIT

WHAT IS YOUR HUMBER AND NAME?

(NUMBER* SPACE* LAST NAME* SPACE* FIRST NAME)

T30 CASEY KAREN

KAREN* SEE ME IF Y0U NEED HELP BEF0RE THE NEXT EXAM. DR. H
PHYSI0L0GY REVIEW #!

INTR0DUCTI0N NECESSARY? (YES 0R N0>
?Nfi

PLEASE ANSWER ALL 4 OUESTI0NS.

I.? VENTILATION
g.TFALSE
3. ?jB

4.72*43

WHICH 0PTI0N?

D FOR DISPLAY.

C F0R CHANGES.

N F0R N0 CHANGES AND N0 DISPLAY.
HELP F0R HELP.

Y0U ANSWERED THE F0LL0WING 2 QUESTION(S) INCORRECTLY.

OUESTI0N GIVEN ANSWER C0RRECT ANSWER

2 FALSE TRUE

3 B A

SEE THE F0LL0WING REFERENCES AND COMMENTS F0R HELP. I WILL PAUSE
AND TYPE A ? BEFORE EACH COMMENT* WHEN YOU ARE
READY FOR ME TO PROCEED* HIT SHIFT/XHIT.

0.2 AND 0.3 PLEASE REVIEW CHAPTER 3 ON ACTION POTENTIAL.

SORRY* KAREN ....BETTER LUCK NEXT TIME.

YOUR SESSION HAS BEEN COMPLETED.
THANK YOU

FIGURE 2

ERIC

v 202

213

R TELLME

-B0J- OTELLME

W0ULD Y0U LIKE RESULTS PRINTED <P) AT C0MPUTER CENTER UR
DISPLAYED ( D) AT Y0UR TERMINAL NOW7 <P UK D)

QUIZ WAS TAKEN 3 TIME(S).

PLEASE TYPE 0NE 0F THE F0LL0WINCI

1 F0R INDIVIDUAL STUDENT RESULTS.

2 F0R FREQUENCY DISTRIBUTION 0F GIVEN ANSWERS.

3 F0R TOTAL NUMBER OF INCORRECT RESPONSES FOR EACH QUESTION.

4 FOR BOTH I AND 2.

5 FOR BOTH I AND 3.

STUDENT HAS ENTERED BOTH NUMBER AND NAME.

TYPE ONE OF THE FOLLOWING*

1 FOR RESULTS SORTED BY NUMBER WITH NAME INCLUDED.

2 FOR RESULTS SORTED BY NUMBER WITH NAME NOT INCLUCED.

3 FOR RESULTS SORTED BY NAME WITH NUMBER INCLUDED.

4 FOR RESULTS SORTED BY NAME WITH NUMBER NOT INCLUDED*

WOULD YOU LIKE SCORES ONLY < TYPE 1>»

OR SCORES AND RESPONSES GIVEN TO QUESTIONS MISSED (TYPE 2).
72

SORTING. . .

CAMPBELL JEAN ID

QUESTION GIVEN ANSWER
3 D

TOTAL NUMBER INCORRECT IS 1

CASEY HARE 30

QUESTION GIVEN ANSWER

2 FALSE

3 B

TOTAL NUMBER INCORRECT IS 2

KRAM ROBE 20

QUESTION GIVEN ANSWER
2 FALSE

TOTAL NUMBER INCORRECT IS 1

QUIZ WAS TAKEN 3 TIME(S).

QUESTIONWCORRECT

ANSWER

2 TRUE

INCORRECT
ANSWER
GI VEN
FALSE

TIMESWTOTAL
bl VEN4TIMES
MtSSEO

3 A

B 1

D 1

FIGURE 3

203

The student*s responses are stored in a file that is available for the course committee to
review at appropriate intervals. The summaries provided include information on individual
student progress as well as class performance (fig. 3).

The resulting systee has been used in several modes, two of which are illustrated in the
following section. The ability of the prograa to adapt to each of these modalities is an
indication of its flexibility, a characteristic that has already led to its adoption by a nunber
of other courses in various departments on the Davis campus.

Physiology 110: ± Comprehensive jjpper division Course

The department offers an advanced undergraduate class in systemic physiology to all
students wishing to enroll. This policy, together with the success of the course itself has led
to an increase in enrollment from 215 in 1970 to 364 students in the fall of 1971. The course is
given through a lecture series supported by eight associated laboratory sections of 24 students
each and 34 tutorial sessions witb from tbree to twelve students.

The concept of team teaching has been thoroughly embraced by the instructors of this class.
Course committee meetings are held weekly to discuss progress, review specific problem areas and
outline material to be presented in the following week. Tutors, most of whom are graduate
students in physiology, participate in these discussions, representing "their" class and
forwarding constructive suggestions for improvements in the course. Tbe responsibilities for
disseminating information and monitoring student progress are thus shared by faculty, tutors,
auxiliary audiovisual aids, and - the computer.

The role of self-evaluation in tbis course is illustrated in Fig. 4. Optional problem sets
are handed to the student at tbe beginning of each week. The problem sets are written to
increase the student*s understanding of designated course material, identify his particular
weaknesses and direct him to further sources for review. These problem sets are thus not tests
but learning aids, used to prepare the student for lecture material that will be presented
subse guen t ly. When the student has completed his review of the problem sets, he enters his
answers through a terminal. The computer scores his work, noting the incorrect responses and
directing bin to appropriate remedial information. The student may then, by finding the correct
responses and discussing his revisions with his tutor, receive full credit for the entire
problem set. A weighted point system provides incentive for the poorer student by offering him
more bonus points for successfully completing the problem set.

While the student is completing his review, the tutors are also able to review the
collective performance of their students, using the summary program described above. They are
tbus in a position to direct the tutorial discussions to areas most pertinent to their class.
They are aided in choosing the appropriate methodological approach tor their discussions by the
weekly meetings of the course committee, during which the students1 problems are reviewed and
the appropriate points for discussion are considered. The task of clarifying difficult concepts
is made somewhat easier for the tutors by limiting tutorial discussions to one week9s material.
The tutors find that this approach offers them a challenge that tbey can meet, and also an
effective means for improving their own depth of understanding of some of the more difficult
concepts. For their part, the undergraduates use the discussion sessions to clarify individual
points that remain unclear after their independent study, to participate in group discussions
about physiology, and to forward information through the tutors to the instructors regarding the
progress of the course.

The problem sets are intended to be introductory to tbe lectures. £ach instructor spends
from three to four hours preparing a problem set that will permit him to extend his lectures
into concepts that reguire an understanding of basic principles. For example, it is difficult
for undergraduates to appreciate the dual interpretation ot certain physiological observations,
such as the sensory encoding of information by the central nervous system. Since the text adopts
the approach of "specific receptors", a problem set was designed to help the student pick out
the arguments used by the author to support his views. The problem set, together with
supplemental reading was followed by two lectures, one which adhered to the interpretation in
the text, tracing specific pathways for receptors within the central nervous system. The second
lecture, delivered by a different instructor, presented an alternative concept reguiring more
complex encoding and multiple sensory pathways as a part of the central nervous system4s
information processing function. Exposure of alternative concepts is greatly enhanced by the
knowledge that students had already reviewed the problem sets and were thus well informed about
the basic concepts prior to presentation of the more complex alternatives.

Introduction of this system came at a time when the campus computer system was just
beginning to accept a full-fledged timesharing responsibility, and a series of problems
accompanied the operation from tbe start, including sporadic malfunctions of the remote
terminals, the host computer and the systems software. Despite these major inconveniences, the

204

FIGURE 4. integration of computer terminals into a large undergraduate physiology course.
A student reviews background factual information (A) ; hears a discussion of r neral concepts in
a large lecture (B) ; participates in a laboratory (C) ; and discusses ideas . * a small tutorial
session. (D)

205

?15

overall reaction of the students was favorable to the system. Their enthusiasm stems partly from
the manner in which this experiment was presented to them, partly from the sense of community
developed by the tutorial discussion sessions, and partly because the program filled a real need
identified by the student. In addition, the program designers worked throughout the quarter to
modify the program in accordance with suggestions made by instructors and students. Several
important changes were implemented in this fashion during the fall of 1971.

£kisi2i sa* il£: A SBgcjli llgd £2H£*£

The School of fledicine at UC Davis offers an interdisciplinary core curriculum supplemented
by departmental electives, one instructor, teaching a class in renal physiology to three
medical and ten graduate students, vas interested in using the self-evaluation system to leasure
student conprehension of the lecture material already presented. Accordingly, he designed short
problen sets for the students to work out within a day or tvo foliosing presentation of the
lecture naterial. The feedback received by the students vas used to guide their study in a
manner similar to that described above. The instructor vas thus able to scan overall student
pertornance and adjust subsequent lectures. A single terminal vas available for the class during
the quarter, and it vas occupied only a small portion of the tine by the class.

Student reaction to the system vas generally favorable in this class as veil. The computer
aid vas highly valued by the instructor. He willingly accepted the additional tine spent in
preparing meaningful comments to be displayed when a vrong ansver vas chosen in viev of the tine
saved by having the computer score, grade, and record results of individual students.

System Implementation and performance

The self-evaluation system vas designed, coded and debugged during the summer of 1971.
Several initial meetings were held to dosign the system early in the summer. Coding vas done in
ALGOi. by one of the authors (GHX) as a part tine activity in the latter part of the summer. The
total effort involved in initial implementation coding vas less than tvo veeks.

After the programs were introduced in the fall quarter, 1971, a number of program
modifications vere implemented requiring an additional veek of design, coding and testing.
Additional changes are planned for the vinter quarter; hovever, the system is fully operational
in its present form and vill be used in several classes during the vinter and spring quarters.

The self-evaluation system meets the criteria of providing a simple entry point into the
instructional use of computers. Hovever, this system is also designed to serve as the start of
a modular development effort. Some of the plans currently under discussion are described belov.

The generation of self-evaluation problem sets vill be expanded to permit representative
selection, vith computer support, of an appropriate group of questions from a library of
problems or questions that has been indexed by subject matter or complexity. Although this step
vould increase the cost for creating problem sets, it might greatly increase the number of
separate problen groups that could be made available to students, alloving a single class to
have more experiences in self-evaluation.

Certain primitive branching instructions vill be introduced, such as skipping past
questions if the performance level is adequate, repetition of certain questions folloving
presentation of more detailed tutorial information than is currently entered, and the acceptance
of more complex vord ansver alternatives. This approach vould not develop into a complete CAI
system, in that specific incorrect responses vould mot he anticipated. Extension to a complete
tutorial language is feasible, but vould be a later step in the development of this system.

The system vill also be expanded by coupling rt to simulation, specially designed
supplemental problem sets or other related learning programs. In this method of learning, one
feedback response from the self-evaluation vould be to call up or recommend to the student a
tutorial program available on the computer. Alternatively, a self-test problem set may be
presented at the end of the auxiliary program to reinforce key concepts.

The problems of computer entry into instructional support can be overcome by simple
programs with effective instructional objectives, one such program system, aimed at providing
students vith self-evaluation through problem sets and furnishing faculty vith details of
student performance, has been designed for use in both large and small classes at UC Davis. This
system vas designed and implemented during the summer of 1971, then introduced simultaneously in

Future Plans

Summary

thrca classes during the fall guarter. Studeat reactions, despite probleaa in the operating
afatea, were highly favorable. The opportunities to attend the ayatea into aore complicated
iaatructioaal aathodologiaa appear proaisiag, but the aaia effect haa beea to gain short tera
benefits without sacrificing either guality or long tera potential, it ia felt that the
under lying philosophy has considerable appeal for inatitutioaa that are juat begioaiag to
consider nee of coaputor support for instruction.

£1?

207

DIMINISHING SQUARES by William (Bud) Bouttote
Problem: Diminishing squares imaginatively developed

319

208

I u GLOVING LARGE ENROLLHENT UNDERGRADUATE INSTRUCTION
WITH COMPUTER GENERATED, REPEATABLE TESTS

Hark Hauer and C. Obert Henderson
Washington State University
Pullman, Washington 99163
Telephone: (590) 335-3507

The Problem

Large enrollment classes are increasingly characteristic of undergraduate education, most
especially for introductory, freshman-sophomore level courses. This trend toward larger lecture
courses has been accelerated by recent budgetary squeezes and the resulting pressure for
improved academic productivity.

When col pa red wicii small classes, large enrollment classes have several serious

disadvantages. For one, they are iapersonal: Socratic dialogue is impossible, classroom

questions are disruptive, and personal acquaintance with instructors is discouraged. For
another, they are insensitive to individual differences: large lectures must be aimed at the
"average" student, with detrimental consequences for both fast and slow learners.

Perhaps the most serious of the large-enrollment disadvantages are those surrounding the
examination procedures which are forced upon instructors by sheer class size, for example, essay
examinations are all but precluded by the impossibility of the grading task they impose. The
typical substitution of "objective" (true-false, mul t iple- ch oice ) tests for essay tests tends to
reduce the intellectual rigor of the course by changing tho required level of learning from
mastery (recall level) to familarity (recognition level).

In addition to changing the level of learning required, the imperatives of large enrollment
instruction effectively force a change in the educational role of the test itself. Tests in
small classes may be utilized prirarily as learning devices which provide both student and
instructor with diagnositc information on the student*s level of understanding. Tests in large
classes, however, are harder to Utilize as learning devices. Tne essay exams, frequent quizzes,
in-class recitation, and rapid feedback which are possible in smaller classes are effectively
precluded for use in large lecture sections; large-class tests are much more likely to be
infrequent (two or three major tests per semester), to cofer correspondingly larger blocks of
subject matter, and to have longer feedback periods (if the tests are returned at all; finals
frequently are not). The cumulative result is that large-class exam inat ions ate used tor
eva luat i on rather than for diagnosis, and the potential value of the test as a learning device
is forfeited. The common practice of posting test grades while not returning tests themselves
concirras the exclusively evaluative role of the examination process.

Finally, large-enrollment tests are likely to be aversive (anxiety-arousing; dissatisfying)
to students. Several factors are responsible for this aversiveness. First, the study habits of
students are commonly observed to follow a "loaf-crara" pattern, with crams coming just before
tests. Second, when exam, are infrequent, the subject matter to bo learned during one cram is
greater. Third, the "perform now or never" nature of the test situation, coupled with intense
emphasis on qrades, creates a high-tension situation for the student. Neither the loaf-cram
study schedule nor the pre-exam anxiety are conducive to effective learning.

Computer Generate Repeatable Testing: A Promising Development

The limitations of large-enrollment instruction have been systematically assessed by
psychologist Donald Jensen, who has proposed and evaluated a variety of potential solutions
(Jensen, 1966, 1968, 1969; Jense: and Prosser, 1969). The most promising of Jensen's approaches
to date is computer generated, repeatable testing (CGRT) .

CGRT encompasses several important changes from typical large-class testing procedures
(Prosser Jensen, 1971). First, tests are given core frequently, typically biweekly. Second,
students are allowed to schedule tests at their own convenience, within broad limits. This is
made possible by the provision of multiple test forms. Third, immediate feedback is provided on
test performance; students are given the correct answers vo test questions as soon as they have
completed a test. Fourth, students can repeat tests until they earn a grade which satisfies
their aspirations. Finally, testing for mastery (recall) is possible through he use of a
procedure for coding responses to fill-in questions (Prosser 6 Jensen, 1971, p. 297).

The procedure usod in CGRT . o accomplish these changes is to prepare a large number of test
questions for each subject matter segment of the course and to read them into a computer. The
computer is programmed to generate independent test forms, each of which contains a stratified
random sample of questions from the bank in computer storage. Thus, literally hundreds of tests

209

can be generated with no two being the same. Having pre-pnntcd a supply ot tests on the
computer (in batch mode), a testing room is scheduled to* be available tor convenient hours
during the exan week. Students nay come in when1 they feel most ready, take an exam, get
immediate feedback, and return to do additional stud y ing if their first score is not satisfying.

Prosser and Jensen (1971, p. 301) have reported that CGRT has been successfully implemented
in several institutions in a variety of subject areas including psychology, economics,
accounting, chemistry, speech therapy, and English. Among the benefits said to be associated
with these implementations are higher student achievement, lowered anxiety and antagonism
surrounding examinations, and better attitudes generally toward botn subject matter and
ins t r uc tors.

iMlcnent i ng CGRT: Our_E x^or 1 once

The theory behind CGRT made sense to us, and we had heard favorable reports on the effects
of repeatable testing from Jensen and others. We decided that it was worth a trial run and
agreed to attempt it. Since both of us anticipated teaching one section of an introductory
Personnel Administration course, we agreed to cooperate in developing CGRT tor both sections.
These decisions were made in the early summer of 1971, and we aimed for Fall semester 1971
imp lement a t ion .

Creating the Test Bank

The first obstacle to be contended with was the required bank ot test questions. Prosser
and Jensen (1971) reported that the number ot test questions available tor any one test should
exceed the number of questions on that test, by six to ten times to assure adequate variation
amonq the test forms. More recently Jensen has said that a 10 to 1 ratio is a desirable minimum
(personal communication). Prosser and Jensen also noted (correctly!) that the preparation ot
this number of test questions is a formidable task.

Since we did not have enough time to create a complete text bank oetore the beginning ot
the tall semester, we adopted a text which had a fairly large numoer ot accompanying objective
test questions. Some of these test questions were contained in an instructors manual and some
were in a student workbook which was available to accompany the test. We adopted the workbook
and included the questions from it in the question bank, thereoy oroviiing students with pre-
exposure to a number of questions over the text as well as with motivation to utilize their
workbooks as study aids. The task of supplementing the questions accompanying the text and of
preparing questions over class lectures was divided among ourselves and a teaching assistant.

Obtaining C >mputer Programs

The second obstacle to be overcome in order to implement CGRT was obtaining the computer
capability needed. We initially anticipated using the system developed at Indiana University by
Prosser and Jensen (1971), but two problems developed. First, a telephone conversation with
Jensen convinced us that it would probably take as much programming time to convert the Prosser-
Jensen system to our computer (IBM 360-67) as to develop our own from scratch. Second, we had
wanted to improve on the Pr osser-Jensen system in several respects, the most important one being
the capacity to stratify the test bank by test item type. Without such a stratification the
proportion of question types on any given test could vary randomly: tne number of true-false
items on a given 20-guestion test might vary, for example, from 7 on one test to 14 on another.
In the interest of achieving uniform difficulty among test, forms, we felt that each form should
have t.he same proportion of question types.

We finally decided to create our own CGRT system. Being snort on both time and money, we
decided to program only the test generation capability, and to postpone the raarK-sense scoring
and computer tallying capabilities which are part of the Prosser -Jensen system. After
specifying the capacities of the program we wanted, we located a computer programmer who agreed
to write the programs for £^00. 00. To our programmers credit and to our delight, the resulting
programs have functioned flawlessly throughout their first semester ot operation. A sample test
is shown in Figure 1, which provides an idea of the format of the tests generated by these
programs.

Developing Policies and Procedures

For testing purposes the 14-week semester was divided into seven two-week units, and a test,
scheduled for each unit. Students were allowed to take a maximum of three (later changed to
four) tests during a six-day period from Wednesday of the second week ot the unit through the
following Monday. This testing interval covered the period from the last lecture of a unit

Z‘> 20

210 ■'

5«nplf ofr$ONNCL TEST
FDP* SO. \o

OUE STICNS

*PUF OP eALSE

i. *> jrp EviuiA^ir*: program can contribute to the improvement of

E^LDYff S A F ET V mIThIN A COMPANY.

?. TwF CONST P’lTtOf n ITV of THE PMP L A BC R SHAPIROS ACT HAS UPHELD BY
Thc tfilTec ^T a Tr 5 $UPPF“E C°UR T 1 N THE *T. CLEMFNS PCTTERY CASE.

3. I* “C ST G’OU0 INCENTIVE S Y STE MS THE IKCENTlVE PAYMENTS ARE NOT SOLELY
rasfo tpov unit? nc poruncTioN.

<•. iHf Ponr,jCTr., LIMITS THAT A GROUP ESTABLISHES POP »TS EMPLOYEES IS
«*<**•.’ AS A ""PGEY."

MULT I PL F CH^ICF

5. Twf r3r c tL F nF jna EVALUATION:

A. INVOLVES thc use "IF THf MANAGEMENT C»P 1 0

l? 'JSeo To evaluate clerical jobs

C. Cn*' T A I'; S CERTAIN FEATURES Cc THE FACTOR CCWPAPISON METhOC
C. P CR w ITS T HE FVALUATIC-N OF BOTH THF EMPLOYEE ANO HlS JOB

6. c F f f C T I VE Fcojujoy i, ] qt R , ThF W I Nl WLM WAr? cpp THOSE WORKING IN

employment crvEPED PPFVIPUSLY BY The fair lapcp STANDARDS ACT became:
a. Il,?0

P. 11.40

r . u.6C
c. n .sr

F III

-IN

TUJ- • SYSTEM of JOB EVALUATION PERMITS JOBS TO BE CLASS I-

Fir»* A*.? GR?UPEC> ACCOPPIN'*- T3 A Sc«IES OF PREDETERMINED WAGE CLASSES
0 F GF^rFS. the c f 2PF A L CIVIL S?«VICF SYSTEM IS AN EXAMPLE CF ThIS

T YPF.

F. WHfN A SA L FS N IS ADVANCED MOncy WhICH ml'ST PE REPAID CUT DF SURSE-

GUP"T Cr““I SSI^VS. hc is S AT 0 TO BE OK A STRAIGHT COmmJSSICn AUGMENTED
KjTu t — .

c. ’ME "SLOPE” AVO thE "ELEVATION" ARE THC CHARACTERISTICS OF A

10.

iNfre th»"

PpnPOR T l^VAL TD

SY ST£ m nF
OUTPUT.

INC ENT I VFS

THE AMOUNT OF WAGES IS OI*ECTLV

NAME

SAMPLE PERSONNEL TEST
FORM NO. 10

RESPONSES

SAMPLE PERSONNEL TEST
FORM NO. to

ANSWERS

1. ITEM 6 1 1 003
ANSWER: _

1. ITEM 6 I I 00)

T C-S PAGE 546.

2. ITEM 6 2 I 009
ANSWER! _

2. ITEM 6 2 I 009

F C-S PAGE 589.

3. ITEM 6 3 I 009
ANSWER: _

3. ITEM 6 3 l 00**

T C-S PAGE 644.

4. ITEM 6 4 l 002
ANSWER: _

4. ITEM 6 4 I 002

T C-S PAGE 601.

5. ITEM ft 1 i 00)

answer: _

5. ITEM 6 l 2 003

C C-S PAGE 56).

6. ITEM 622 004

answer: _

6. ITEM 6 2 2 004

C C-S PAGE 587.

7. ITFM 6 I 3 005
ANSWER: _

7. ITEM 6 1 3 005

D JOB GRADE PAGE 548.

e. ITEM 6 1 3 008
ANSWER :

9. ITEM 623 005

answer: _

10. ITEM 6 3 3 002
ANSWER :

P» ITEM 6 l 3 008

M DRAWING ACCT. P 610.

9. ITEM 6 2 3 005

V WAGE CURVE LEC 11-12.

10. ITEM 6)3 002

C PIECEWORK PAGE 604.

FNP pf tfst

FOR* no. 10 SAMPLE PERSONNEL TEST

FIGURE 1.

Percent (Number) Responding

CGRT

Rating

Much

Worse

Considerably

Worse

Slightly

Worse

Average

Slightly

Better

Considerably

Better

Much

Better

After 2nd

7.0

5.6

7.0

25.4

36.6

11.3

CGRT Test
(N-71)

(5)

(18)

(26)

(8)

After 6th

1.6

3.1

7.8

9.4

31.2

28.2

18.8

CGRT Tes t
(N-64)

(1)

(2)

(5)

(6)

(20)

(18)

(12)

TABLE 1. Student Ratings of CGRT v. Conventional Tests

Number of Students (N*81)

Grade

Test 1

Test 2

Test 3

Test 4

Test 5

Test 6

Six- Test
Average

h 29

TABLE 2. CGRT Grade Distributions for Six Biweekly Tests

until the first lecture of the next unit (students had two lectures and one small discussion
grou p week 1 y) .

A testing room was manned by an instructor or an assistant for six different scheduled
periods, including one period Saturday evening and another Sunday evening. Testing room
procedure called for a student to sign for a test in a log book and to indicate there his
discussion section and the form number of the test he received. Upon completing the test, the
student would cut the "Responses'1 column from the test questions (Figure 1) with a pair of
scissors provided, and hand it to the instructor on duty. The instructor would take the
"Answers" column, which had been previously cut off, line up the correct answers with the
student's responses, and grade the student's test. This grade vas then marked on both the
"Responses" column, which was kept for recording, and on the "Answers" column, which was
returned to the student.

Having agreed that an arbitrary, pre-established criterion schedule tor grading was
preferable to the use of grade "curving" we adopted a fairly exacting standard, viz., 95%* - A,
90%* = 3, = C, 8 Q% + = D, and below 80% = F. Me assured ourselves that students could be
expected to attain levels higher than are typically demanded because: a) some of the test
questions used were taken from their workbook, giving them a pre-exposure to some items, b) up
to half of the test questions were of the True-False type, and c) any chance variation in test
difficulty worked in the students' favor since only the highest test score was counted. Even
with these considerations the grading standards seemed to us plenty rigorous, but we reasoned
that we could be lenient in final grading if they turned out to be too demanding.

Twice during the semester feedback was solicited from students on several aspects of CGRT.
The first sot of student ratings was obtained in the fifth week of the semester, which was just
after the second CGRT unit test; the second set was gathered in the thirteenth week, after the
sixth tost. Both sets asked for open-ended comments on several specific goals and mechanics of
the CGRT technique, as well as an overall evaluation of CGRT.

The ooen-ended responses were favorable overall, with two exceptions. Specifically, the
responding students practically all had favorable responses to inquiries on fairness in
evaluation and grading, repeatability, frequency, studen t-sched ul ir.g , and availability of
immediate feedback on per f ormatice. There was also substantial agreement on two criticisms of
our CGRT program: test unreliability, and excessively high grading standards. Both of these
criticisms will be discussed below.

For the overall evaluation, students were asked on both occasions to rate CGRT "in
comparison with other testing procedures you have seen" on a 7-point scale from "much worse" to
"much better." The student responses are summarized in Table 1. On the average, students rated
CGRT "slightly better" on both occasions (mean scores were 5.0 and 4.8 respectively). However,
Table 1 shows that the distribution of ratings shifted from the first to the second evaluation;
while the modal response decreased from "considerably better" to "slightly better," the number
of "much worse" and "considerably worse" ratings decreased and that of "much better" ratings
increased. Additionally, students were asked on the second evaluation occasion to indicate
whether they would choose a class with a) CGRT or b) Conventional testing, if all other things
were equal. Of 64 answering students, 49 (or 77%) chose CGRT.

Student performance on tests has exceeded our expectations. Table 2 shows the grade
distribution for each of six tests that have been administered to date, as well as for the six-
test average grades. There seems to be a general trend toward higher grades, and after six
tests the distribution of average grades is skewed upward with a distinct mode at the "B" grade
level.

Our initial expectation was that our achievement standards might have been too high. Our
early doubts we amplified by student responses on the first questionnaire; many students
complained that our standards were too high and unrealistic. However, after six tests, almost
two-thirds of the students have averages of " B" or better. It appears to ns that the
distribution of final grades will be higher than the distributions either of us has seen
recently in this course.

However, our standards ma^ be too high. It is quite clear to us that the higher grades
reflect a considerably higher level of effort on the students' part.’ *e asked students on the
first questionnaire how much time they were spending on this course, and how this time compared
with that spent on other courses. Of the 60 responding, 2 claimed they were spending less time
compared with 54 who reported they were spending more time. Whether or not it is legitimate to

Results

Student Attitudes

Test Performance

utilize techniques which effectively extort a disproportionate amount

time is a question with
con t roversial.

which we have only skirmished, but

of the student's study
which appears likely to be

We had expected some expression of resentment on the questionnaires over the increased
study time which students were devoting to the course. To our surprise, the students generally
expressed gratitude for being alloweO the opportunity to improve their scores by repeating
tests. Given the overall favorability of sentiments expressed and the pattern of test
performance observed, it seems clear to us that our stj
it better ?

learninu devices which stimulate further study.

relate to us as helpers.

with our experience.

To illustrate: we suspect that a substantial number
point averaqes of "C" or lower really prefer to think of
Professors who have observed closely the typical po
agree, however, that inferior performance doesn't necess
Because there are so many good, plausiole explanations
questions," "incompetent instructor," "lousy text," "tes
sleep a.l last night)," "my great aunt died," "my gir
familiar rationalizations (and countless others) are all
convince themselves and others that they are really bett

its are

both lea

rni nq more

and

liking

», sever

al other

Dhenome na

associated

» that CGRT has

el imi na ted

great

.ng eXDe

r ience.

Students c

ome

to the

They frequently

ask quest

ion

s bot h

ionse to

i naving

their tests

aded is

>rt, tes

ts are really tunct

io:i

inq as

»nt attitudes to

ward the in

str

uctors ,

than i

n an adversary role

Having

‘ttled on a fixed and exact

ing

set of

|e each

student

to do his best

• When

e does

poorly ,

his disappe

in t

ment is

i their

side and

appear mo;

e p

rone to

ts are

becoming

aware that

they have

is real

iza tion

is coupled

th the

e is earned, t

he effect i

s t

hat the

ina t ed.

Ve e

mphasize t.

his

point

ibser vat

ions to

be made in

conn ect ion

college

student

s having ac

tua

1 grade

msel ves

as "A

" or " B"

uden ts.

xaminat

ion beha

vior of stu

den

ts will

y threa

ten one'

s self-ima

ge.

Why?

for poor per form ince: "Misleading test

ting room too hot," "headache (didn't
1 left me and I'm all messed up." These
invoked by students to effectively
er students than the record indicates.

None of this nonsense is effective under CGRT , and we think that this may explain much of
the increasing scarcity of C's, D's, and F's in our grade distributions. Interestingly enough,
a number of best students have shown signs of the same effect. Some seem quite incapable of
settling for anything less than a perfect score. For example, students who have earned an A (19
ot 20 correct) frequently return a second and a third time in attempts to make the perfect
score.

Test Reliability

It was mentioned earlier that test reliability was the subject of considerable student
criticism. It seemed that students all too often received lower test scores in spite ot greater
preparation. our perusal of the patterns of test scores confirmed that there was at least some
problem, since there were occasional instances in which a student would get, for example, a B on
the first test followed by an F on the second. We were therefore led to investigate the
realiability problem further.

We did a check on the test-retest reliability of one of the CGRT unit tests using four
different groups of students. For a class of 112 freshman and sophomore Introduction to
Business students, the reliability coefficient, was .25. Reliability for a group of 23 advanced
personnel students was only slightly better at .38. The highest reliability was obtained with a
group of 14 MBA students, where the figure was .61. Finally, students in the present CGRT
course were given two tests during one class period (both for credit) , and the resulting
reliability figure for these 76 students was .46.

These reliability figures were disappointingly low. The students were all too right -
apparently the process of randomly selecting test questions from an item bank results in a wider
variation in overall test difficulty level than we had anticipated. As a result ot this
information we have been thinking about ways to improve test reliability. The most promising

2 B9u"

approach now seens to us to be that of stratifying the question bank by, concept, rather than by
textbook chapter or by time period (e.g., Week 8). This procedure would have the effect of
reducing the variance in test difficulty attributable to variance in topical coverage. We are
beginning to think more in terms of clusters of fairly equivalent questions being associated
with each key objective or concept to be covered. Of course, a second sure-fire way to improve
reliability is to increase the test length; so far our tests have had 20 questions each.
Whether or not the increased reliability of a 30-question test would offset the disadvantages of
the longer test is not yet clear.

Possible Im£l ica t i on s of CG^T

The following speculations are offered to suggest the range of Potential impact possible it
CGRT proves successful.

1. Nany large-enrollment, introductory courses have multiple sections and multiple
instructors, and it is no secret, among students at least, that substantial differences exist
ameny sections which are attributable to different instructors. It seems to us that there are
too many instances of multiple-section introductory courses where substantial differences in
course content exist. Where a certain course is a prerequisite to others, or is required tor a
major, substantial differences among sections of multi-section courses cause untold problems for
instructors of advanced courses and student advisors. Clearly, standardization of courses at
the introductory level is needed.

The possibility of cooperation among instructors for the purpose of developing a test item
pool for a course suggests cooperation in defining the goals for the course. It seems
plausible, if not likely, that instructors should be able to reconcile whatever differences
exist among themselves and agree on specific course goals and the associated test pool questions
and criteria for satisfactory performance.

One interesting question suggested by the above is "What w
to require that instructors assigned to a certain multi-section
in establishing a mutually acceptable set of course objectives,
of satisfactory performance?" Surely some groups of instructor
inconvenience; almost as surely as some could not. However
where irreconcilable differences exist are precisely those where
is appropriately exercised to eliminate minority individua
E2i2£tory course. This may sound severe, but it boils down
that introductory courses should concern themselves with consens

ould happen it a department were
introductory course participate
a test item pool, and the level
s could do this with little
, it may De that those instances
de par tmen ta 1- level intervention
Is or factions from teaching t he
to the reasonable proposition
us- level subject matter.

This should not be taken to imply that the course in question should be highly structured
in either content or method; one group of instructors might, for example, decide that their
"consensus topics" should constitute 25% of the course requirements, and the remaining 75% would
be open to the individual instructors preference. Furthermore, the raetnods used by the
instructor to cover the consensus topics would be quite open.

2. If the development of consen sus- level test item pools is a practicable possibility, and
these were to become available for major undergraduate courses, a number of interesting
advantages might be realized. For example, take a transfer student who had taken an
introductory math course at another institution: he is satisfactorily prepared to begin work in
advanced courses? The availability of consensus test pool would make it possible to give the
student a subject matter mastery test which would pinpoint any areas of weakness.

Such tests might be useful in determining whether students should be given credit for
various combinations of prior work.. The effect of such a practice might well be to shift the
criteria for acceptability from such arbitrary consideration as, "Was his institution
accredited?" or "What text did he use?" or "Where and when did he take the course?" to "Does he
now understand the critical concepts?"

3. Another major advantage of the existence of CGRT tests would be that superior students
could be invited and challenged to proceed at their own pace and to demonstrate their competence
as soon as they are ready.

4. A further implication of the widespread availability of CGRT test item banks is that
independent and off-campus study could be greatly facilitated. If course objectives and
requirements were specified and made available along with sample CGRT tests, all eligible
applicants could be invited to demonstrate their competence on any available CGRT test, and to
claim credit and advanced standing for doing so.

Incidentally, CGRT tests would seem to be ideally suited to correspondence study. For one
thing, numerous sample tests could be provided to the correspondent-student. For a second, the
immediate feedback on test performance possible with CGRT would be a dramatic improvement over

ERIC

225

r *

215

the long-delayed feedback typical of correspondence course tests. Finally, the use of the sane
CGRT exans being used in parallel courses on canpus would insure the conparability of the two
courses in subject natter coverage.

5. CGRT appears to be highly compatible with several concepts associated with the audio-
tutorial approach to learning (Post le thwai t , Novak 6 Hurray, 1969). Student scheduling,
repeatability, and prompt feedback from frequent quizzes are features of both. The concept of
providing mini-courses and requiring learning for mastery (Bloom, 1969) suggests that CGRT test
pools could be geared to mini-courses and the criterion level stated. Furthermore, specifying
objectives in behavioral terms (Hager, 1962) is a step which should naturally precede
preparation of the specific test bank items which operationalize those objectives.

Further Development Anticipated

CGRT has been surprisingly successful, and we have plans tor expanded implementation and
for more systematic experimental evaluation. Hark Hammer has recently received a 112,000 grant
to develop a more sophisticated CGRT computer system and to give CGRT a more thorough evaluation
compared with conventional testing techniques. As one result of this project, computer programs
and documentation should be available by September 1972.

REFERENCES

1. 5loom, R. S. , Learning for mastery, UCLA CSEXP Evaluation Cogent, 19S8, Vol. L, No. 2.

2. Campbell, Donald T. , and Julian C. Stanley, Experimental and quasi-e xper imen ta 1 design for
research in teaching. In N. C. Gage (ed.). Handbook of Research in Te^h^ng. Chicago:
Rani McNally, 1963.

3. Hammer, Hark A., C. obert Henderson, and LeRoy Johnson, A report on tour techniques for
improving large enrollment instruction. Unpublished summary of report given at Northwest
Universities Business Administration Conference, Portland, October JO, 1971.

4. Jenson, D. D. , Testing and large class instruction. l£2*l h and Change at Indiana

University* 1966, Vol. Ill, Section XLI. ”

5. Jensen, D. D. , A system for improved large enrollment instruction. Unpublished manuscript,
Indiana University, 1968.

6. Jenson, D. D. , An efficient, effective, and humane system of large class instruction.
Unpublished manuscript, Indiana University, 1969.

7. Jensen, D. D. , and F. Prosser, Computer-generated, repeataole examinations and large class
instruction. Paper presented at Midwest Psychological Association Meeting, Chicago, 1969.

3. flager, Robert F., Prepa rin g Instructional Objectives. Palo Alto, Calif.; Fearon, 1962.

9. Postle th wait , S. N • , J. Novak, and H. T. Hurray, Jr., Th» A u .1 io-Tu tor ia| Approach

Learning, 2nd. ed. , Minneapolis: Burgess Publishing Co., 1969.

10. Prosser, Franklin, and D. D. Jensen, Computer generated repeatable tests. APIPS (American
Federation of Information Processing Societies) Conference Proceedings, 1971, 38, pp. 29b-
301.

216

AN ANALYSIS OP THE USE AND EFFECTIVENESS Of EXAMINER - A COMPUTERIZED QUESTION BANK
AND EXAMINATION PROCESSING SYSTEM - IN COLLEGE OF BUSINESS COURSES AT THE UNIVERSITY OF

SOUTH FLORIDA

Stanley J. Bickin
University of South Florida
Tampa, Florida
Telephone: (813) 974-2960

Introduction

A considerable nunber of the undergraduate "core" courses in the College of Business at the
University of South Florida are taught to large classes with as many as 250 students in a
section. Such an arrangement presents the instructor with enormous problems concerned with the
presentation of the course material itself and also with the adminis tra t ion of the course.
These administrative problems include: (1) examination preparation and administration; (2) class
handout preparation, and distribution; (3) grading of examinations and various handed-in
assignments; (4) providing the student with feedback as to "how he stands" in the course; and
(5) determination of the final course grades based on overall performance. This paper deals with
a computerized approach designed to alleviate the first of these administrative problems namely
that of preparing and administering the examinations in the course. The paper reports on the use
and effectiveness of the EXAMINER system which was designed and made operational by the author.
The system has been used in the preparation of examinations for the PhINCIPLBS OF MANAGEMENT
courses and the COMPUTERS IN BUSINESS courses over the past four academic quarters.

The Need for Ira£rqvemen t

The impetus to improve upon previous methods of examination preparation and administration
came from throe directions. The first was that the sheer size of the classes (in terms of
numbers of students) meant that the examinations were typically of an objective nature and
involved multiple-choice and/or true-false questions. Each time the course was taught the
instructor had to, (a) compose new questions, or (b) draw upon questions from previous
examinations, or (c) use questions from the instructors manual or some other source. An
informal survey showed that many instructors kept a card index file containing their "favorite"
list of "tried and true" questions. Selections of questions from these files, coupled with
additional questions from elsewhere were used each time an examination was needed. This involved
considerable amounts of retyping of questions each time an examination was prepared. The second
was that large classes are often conducted in either a room or auditorium in which the students
sit close together. Consequently, there is always the opportunity for a student to observe the
responses marked by nearby classmates on their answer sheets. The third direction was that the
demands for secretarial work in the department were such that examination preparation involving
typing, duplicating and collation had to be minimized.

The EXAMINER System

EXAMINER is a two-phased system. Phase I involves the establishment and maintenance of a
computerized question bank. Questions are punched on to cards in a fairly free format style and
become part of a permanent card, tape or disk file. This provides a readily accessible means of
retrieving questions for processing by the second part of the system. Phase II is the
examination processing part of the system and operates as follows. On request, the EXAMINER
system produces for the instructor in normal examination format a numbered listing of all or
some of the questions in the bank. From this list, the instructor selects (along with an
additional group of questions not currently in the bank) those questions he wishes to include in
the examination. These question numbers are punched into predetermined fields on standard 8U
column cards. Required headings for the examination and also instructions to be included at the
beginning of the examination are punched on to standard 80 column cards. An EXAMINER control
card is punched which provides information such as:

a. How many copies are needed?

b. Is the examination to be produced in two parts with a certain group
of questions in PART I and a second group in PART II?

c. Should the examination be produced in a single-print format (in
columns 1-64 of the paper output) or double-print format (with two
examinations printed side-by-side on the paper output in columns 1-
65 and 68-1327

d. How many different times should the questions be scrambled? The
systen provides for up to a maximum of four different scrambled
styles of presenting the same question.

A complete listing of the computer system job control language (JCL) cards, and the EXAMINES
control and instruction cards for a saaple run is given in Appendix a. The output produced by
this sample run is shown in Appendix B. A saaple answer Key produced by EXAMINER is presented in
Appendix C.

The physical reproduction of examinations by EXABINER can be performed in one of two ways.
The first way, and that used at present at the University of South Florida, is to request the
EXAMINER system to print sufficient copies for the entire class. Using aul ti pie- part paper and
the side-by-side, double print format feature 200 copies of a twenty page examination typically
has taken approximately 20 minutes on the high speed printer. The advantage of this method is
that after removing the carbon paper and bursting the multiple copies, the examinations are
ready for stapling together and do not have to be collated page-by-page manually. The second
way is that the EXAMINER system can be used to produce a single master from which the exami-
nation can be reproduced by conventional duplicating methods.

St udent Reactions to EXAMINER

A survey of over 200 students enrolled in courses using EXAMINER gave some indications of
student reactions to the systen. The students were asked to respond to four forced-choice
questions giving their opinions concerning EXAMINES. The results of the survey were as follows.

£H£Stion JL vnen you took your first examination using EXAMINER did you find that its
"computer format" appearance was a distraction? The survey clearly indicated that the initial
encounter with EXAMINER causes some distraction because of the appearance of the examination.

Response to Question 1.

Definitely
To an extent
Only a little
Not at all
No, it was a help

Total Responses

Just under half of the students
varying degrees by the appearance of
distraction at all, and 14.5 per

the

sys t

Res£onse to Question 2
Yes

Stayed the same
No, it increased

Total Responses

Numbey

Percentaqe

9.4

9.9

27.2

39.0

14.5

212

100.0

>.5 per cent) believed they wore d

:iou. However, 39.0 per cent i

respondents indicated that the cl<
in •

you took

which were prepared by

l ( if o ne

existed) diminished?

N umber

Percen taqe

37.7

46.7

15.6

212

100.0

reported no

This question was designed to determine if any distraction caused by examinations produced by
the EXAMINER system decreased as the students became familiar with computer produced
examinations. As the responses show, over a third of the students in the sample 37.7 per cent
believed this to be so. Also 46.7 per cent reported no change in the distraction level as
subsequent examinations were taken.

3. As far as the quality of the reproduction of the examinations produced by
EXAMINER is concerned did you find that they were legible?

A follow-up on a sample of the 31 responses indicating that the examinations were poorly
reproduced showed two sources of concern. The first was that the carbon copies produced using

five-part paper were faint and hard to read in

a large auditorium

with only limited

lighting

facilities. The second was the use of all upper

case characters

in the printing

of the

examination. The first of these problems has already been remedied by

the

Response to Question 3

Number

Percen ta qe

Definitely so

23.7

Reasonably so

133

61.9

No, poor reproduction

14. 4

To^.al Responses

215

100.0

use of/ three-part paper with good results. The second problem has not been resolved at this
time. ,An extension of the EXAMINER system to incorporate upper and lower case characters using
special print train on the printer would provide one solution to the problem.

/Question 4. rfhat is your overall reaction to t aking' exaainat ions produced by EXAMINER?

/ ■

Respgnse to Quest ion 4

Favorable
Neutral
Unfavorable

Total Responses

Number

Percen ta

30.7

46. 1

23.2

215

100.0

Since the EXAMINER system is an administrative program designed primarily to benefit the
instructor rather than the student, the percengage of favorable and neutral responses to this
guestion is regarded as highly encouraging.

Summary

The EXAMINER system can be an extremely valuable approach to improving the administrative
effectiveness of the examination preparation process. The major benefits result from four
features of the system.

1. The maintenance of a permanent guestion bank for a given course, which provides
an easy method of preparing an examination by selecting questions from the
question bank.

2. The reduction in the amount of secretarial typing, reproducing and collating of
examinations.

3. A reduction in the opportunities for cheating of scrambled styles of producing
the same examination.

At this time details of the cost effectiveness of the EXAMINER system are not available. A study
of the comparison of the cost of computer versus manually produced examinations is underway. It
is hoped that such a study will reveal even more additional long-range benefits of the EXAMINER
approach to computerized examination processing and question banks.

Or ' -

2S9

PARTHENON by Tom Fong
Problem: Redundant serial imagery

A COMPUTER-/SSISTED ,1 t'THOD FOR TEACHING LARGE ENROLLMENT LECTURE
SECTIONS: THT BIOLOGY PHASE ACHIEVEMENT SYSTEM (PAS)

K* (>. fLanke, W. D. Dolphin, G. F • Covert
Iowa State University
Ames, Iowa

C. D. Jorgensen
Bnqhaoi Young University
Provo, Utah

Int roquet ion

Iowa State University initiated an interdisciplinary undergraduate program in biology at
the beginning ot the academic yor»r, 1969-70. This new program substituted several new biology
courses at the freshman level for redundant introductory courses in botany and zoology. One of
t lie new offerings was a lecture course, Principles ot often taken as the first course

in mology at the University by -majors and non- raa jot 3.

of il±2l22I grew quickly. Lecture sections of 300 to 6U0 students were created to
accommodate the large enrollment, a total of 3541 students m the 1969-/0 academic year, and
3571 students in 1970-71.

The shortcomings ot tntf teaching and administrative procedures followed in this and many
other largo lecture courses soon became obvious. As a result improved methods were sought which
would meet. the problems in oiology and possibly be applicable to large courses in other
disciplines too.

Teach i n g/ lea rn i ug inadequacies in these sections included the following:

the lack of student individuality in the learning situation. Highly motivated or
veil- prepared students were often bored with the material presented. Ill-prepared or
slow-learning students were too often overwhelmed. Consequently, a method was desired
which would allow students to set their learning pace in accordance with their
background and ability.

the dependence of the student on the lecturer and textbooK tor his biological
information. Instructors felt strongly that learning should primarily be an
enterprise of the student and that the purpose of tne lecturer was to guide the
student's search for information rather than primarily to provide biological tacts
and princip1. es. A method was needed which would encourage the student to use the
instructor, the Look and other facilities as resources to be consulted for answers to
specific questions.

tne competitive grade-oriented structure of the college biology experience. The most
valuable expenditure of time and energy for students was felt to be the individual's
increase of Knowledge over his previous level of learning. Therefore, a system was
desired wherein the student would compete in learning with nimselr and no; with
ot he rs.

* d min is tra t i ve problems included:

1. record keeping. Most instructors usually administered three exams per term. Grades
from these exams were totalled, "curved", and letter grades assigned. Consequently,
much time was spent on record keeping rather than teaching.

tne development of exams. Exam production took many hours. Numerous forms were
reguired because of the crowded lecture halls, and usually elaoorate precautions had
to be taken to insure security.

3. the lack of any systematic and easy assessment of the new program. The young program
was felt to need constant evaluation so as to know where strengths and weaknesses
lay. Furthermore, large numbers of students in the basic program seemed to present an
ideal situation for obtaining date on basic teaching/learning problems. A means had
to be created to secure data systematically and easily.

An attempt to meet these problems resulted in a system of teacning large groups in the
basic biology course. Principles of n iology, using computer assistance. The system, known as the
Phase Achievement System (PAS) , was developed jointly by the Biology Program and the Computer
Center at Iowa State University using the Test Scoring Service facilities.

221

Thi« Method of PA^

In order to
developed to handle

implement PAS, the course content vas modularized and computer
the record-keeping and the exam compilation and evaluation*

programs

mere

Course Content

The course content of Princjp les of Biolc ;x was ari inged into eight areas, each centered
around a conceptual theme* These eight areas, or phases , were

1. structure and Evolution of the Cell

2. Cell ilar Metabolism: Catabolic

3. Cellular Metabolism: A nabolic

4. Mitotic Cell Division and the Development
of Mul ticellularity

5. Reproduction

6. Genetics: Inheritance

7. Genetics: Molecular

8. Evolution

Por each phase a set of behavioral objectives was constructed. This mas a tine-consuming
project forcing extensive examination of the definition and purpose ot Principles of Bio log y by
individual instructors. After the course objectives mere formalized the students mere given
copies a;?d told that these represented the material of the course. The student was then free to
use whatever resources the University had to meet these objectives.

Multiple choice examination questions correlated with the behavioral objectives mere
written and collected for each phase. Eventually over 3,000 questions were accumulated tor all
phases. Besides being grouped hy phases, questions were subgrouped into 10 topic categories
within a phase and difficulty estimates assigned to each question on a 1 -10 scale of decreasing
difficulty. Eventually difficulty estimates will be objectively assigned on the basis of the
p rcentage of the students answering the question correctly.

With the modularization and definition of course content and the adoption of a standard
pool of test questions the following procedures were adopted:

1. Lecture schedule and detailed course objectives were distributed to students.

2. At the beginning of the term a short test over each phase, a ’’Test Out exam,** was
administered. Each phase test contained 15 questions, the exam containing 120
guestions. Any student who passed seven out of eight tests could at this point
receive course credit if he desired. Students who passed less than seven out ot eight
tests attend lectures in order to prepare themselves tor the next exam. By the end of
the quarter students had to accumulate passing grades on seven ou* of eight phases in
order to receive a passing grade.

3. At each two-week period throughout the term an opportunity was provided tor the

student to re-take an exam over any phase not previously passed, or passed with a low

mark. Thus, a student was provided with the opportunity to re-take any phase exam in

an attempt to pass a phase or raise a grade on a phase exam already taken. In a ten-

week terra a student had the opportunity to take an exam six times over each of the

eight phases. The plan allowed a student to arrange his own exam schedule.

4. Students’ grades were assigned only when passing scores were ■ a t tained on seven of the
eight phases. A score of 53% was "passing” on each phase. Students who completed at
least four of the seven phases, and who took exams over other phases but did not pass
them, were eligible for a grade of Incomplete (I). To receive this grade the student
signed a written agreement accepting an Incomplete. Any student receiving an
Incomplete was allowed another tern to pass e^ams and bring his record up to passing
seven out of eight phases. These procedures are illustrated in a generalized flow
chart in Figure 1A.

Com pu ter Assistance

Two computer processes have been developed to support the
the scorer and record keeping process, aad the test generator
processes from a usage point are detailed below.

curricular innovations,
process. Descriptions

These are
ot these

uttcra » THt maii achiivhimt svsran rui

Of im HOiOtV NOIMM 0# TNI COUIM Of KIlNCII AMO NUMUTtll
AT IMA IT ATI UKIVIUITV AMIS. IMA

FIG 1-A

FIG 1**B

MAI f MOM ITVMMT* t VIIMMCIKT

piom of mas mmx hi

FIGURE 1. The overall flow of the Phase Achievement System.

A. Sequence of events followed by students enrolled in cpurse.

B. Sequence of events involved in testing and scoring of students.

223

2&S

STUDENT

REC0805

FOR B

I0L

31 P

EXAMS

DATE : 09/NOV /

SSN ZE

PHZ

347<.68066!?

1110

<.7

20..

_34 746 84 20.1

1110

3475646570 .

1110

3476607307

1110

6 0

3478626850

1110

Fig. 2, An example of instructors* cuaulative record of five students. Abbreviations: SSN,
section numuor and then nine digits of social security number; Z E, Security function, a digit
appearing here means student record has been alterred by other than test input; NP, nunber ot
phases passed to date; SC, studcnt*s average only on those phases passed; PHZ 1-B, students
scores or nhase tests taken. These records are taken after third exam period. Further scores
earned by students will be entered below these scores.

PATEM5Z-N0^/7.I‘

SSN

SCORE

3481586420

80*100

87*

73*

3481626696

40#

3481642803

33#

3481649392

3481680898

87*

47*

3481686670

20#

4 0#

3481700996

47*

73*

53*

80*

3481705455

6 7

47*

07*

53*

Fig. i. An example of exam results as posted. Abbreviations as in Fig. 2. Lntnes without
superscript were carried forward from previous exam. Entries with * or l represent scores froa
current exam. A * means current score is highest score earned to date. A # aeans current score
is lower than a score previously earned on particular phase. Average is based on highest
passing scores earned on a phase regardless ot whether score is printed or not.

4»

OVERALL FLOW OF THE PAS PROCESS

Pig* 4* Flow chart of generator and scorer programs showing iaputs to various prograas* Raster
record contains constants relating to nuaber of phases, nunber of questions per phase, passing
levels, relative weights for each phase (one is used for each phase in case discussed) etc*
Prograas are highly adaptable to other courses or changing courses with this provision*

( ,

225

335

ANALYSIS OF THE ELEMENTS OF A GRADE

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The Scorer and Record Keeping Process. Students taking an examination pencil mark
standard IBM Form 511 multiple choice answer sheets. Student entries on the tori give
the student’s social security number, the test identifier, and the answers to the
questions in set fields across the paper. When submitted the answer sheet is
processed through an IBM 1230 Optical Mark Reader which reproduces the student
responses on a machine readable punched card.

The punched cards representing the tests
£ • S« U* Computation Center* Student records kept
numbers are output in three formats. A magnetic
the current examination and later serves to be th
Three printed records are created. One is a
instructor (Fiy. 2). Another is a record of the r
plus the highest grade previously earned on a
Symbols appropriately designate the source of a g
record is an exception listing* Anytime an examin
ot students fail to or wrongly encode their socia

e not scored but
cate of the pu

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are scored on the IBM 360/65 at the
by section and social security
tape is used to record the output of
e starting input in the next exam,
cumulative record and is used by the
esults of the current examination
phase if there is no current score,
rade (Fig. 3)* The third printed
ation is scored a certain percentage
1 security number or key identifier,
are placed on the exception listing
nched card. When the record is
update commands given to the master

is set up to add, delete, or partially modify records in
hrough mark sense cards that can easily be encoded
nd submitted at a later date.

Test generator Process. Programs have also been developed to use the 360/65 in
compilations of the ex^ms. The previously prepared question pool was entered on
magnetic tape. Questions were grouped oy phase and by 10 topical areas within a
phase, bach taped question had associated with it: (a) a unique identifier, (b) the
question and responses, (c) the correct answer indicator, (d) a difficulty estimate.
The unique identifier allows statistical information on a question to be stored for
lateL evaluation.

Tests were constructed by generating random numbers which were used to choose a
question in a topical area. Topical areas had one or two questions chosen from them
to construct a phase test of 15 questions coveriug 10 topics. A key was simul-
taneously generated to be used in the scoring of the test. Each generated test had a
cumulative difficulty rating derived from the sum of the difficulty of the questions.
Instructors used this to screen overly difficult or easy tests. If a test was
approved it was sent to the copy center where the required number of copies was made.

A flow diagram in Fig. IB and 4 summarize these points.

With the subject material and grades modularized it is now possible to
internally monitor the effectiveness of the teaching/ learning situation. Average
scores earned on a phase can be compared thus creating a feedback loop to identity
problem areas in student performance. Appropriate corrections than can oe made in the
objectives, testing, or instruction to insure subject material competence.

Advantages of PAS

The

PAS has provided

solu t ions

to pr

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eachii

advantages include th

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the material a

deficiencies in biology lie and can efficiently use his time on these areas*

studen

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ows where

his

i. The jrade earned represents the mastery ot an amount of biological information. A
student is required to have a broad understanding ot biology as well as depth in 7
out of 8 areas (Fig. 5, 6). This degree of knowledge is not necessarily assured under
the traditional method ot teaching.

4. because ot the retesting provision, competition for grades among classmates is
eliminated. Rather a student competes only with himself against standards set by the

ERIC

237

instructor and outlined in the objectives. Grades reward student enterprise rather
than intelligence.

->• The responsibility tor learning rests on the student. The instructor is no longer in
the central role, but rather is one of several sources of in forma ti on.

(». Record Keeping is facilitated, and instructors teaching great numbers of students are
freed from this chore.

7. Time spent on exam compilation is minimized.

d. Computer listing allows for ready and easy accessibility of data for studies of basic
teachiug/lear n ing proDlens and evaluation of subject areas within the course.

PAS is readily adaptable to courses other than biology. Plans are underway to adapt
it to other large enrollment lecture section courses at Iowa State University such as
those in the Departments of Earth Science and Library Science.

<538

* » # pA

OPERATIONAL ASPECTS OP COBPUTBR NRITTEN AND SCORED
FIRST YEAR COLLEGE ACCOUNTING PROGRESS EXABI NATIONS

MICHAEL BALDIGO

INDIANA UNIVERSITY
BLOOB I NGTON , INDIANA 47401
TELEPHONE; (812) 339-1069

Summary

The following observations are collected from the experiences of the author in using
computer written and scored objective progress examinations for first year college accounting
courses in 1970-71. These are not just classroom observations nor computational aspects of the
data processing; the discussion centers on the administrative tasks of distribution , control ,
and student-system feedback in handling nearly 800 weekly exams for three concurrent accounting
courses , each divided into numerous discussion sections. No firm conclusions arise from these
observations , but a number of insights and guideposts are suggested as to the planning one would
do in tapping the computer's vast information processing capabilities to meet more effectively
one's own educational requirements.

Progress examinations present a painful set of sacrifices in teaching effectively,
particularly for required business program courses such as accounting A201-202 and for popular
electives like accounting A200. Progress exaainations, or a reasonable substitute where
possible, are highly desirable in aaintaining a studentas interest, aotivation, and sense of
commitment and cumulative progress. Yet they are an increasingly high-cost, labor-intensive
effort, which coapetes directly with time for instruction and preparation.

On the horns of this dilemma, the teacher can re-stretch his resources and attempt to
write, grade, record, distribute, and discuss such exaas by hiaself or with relatively little
incremental assistance, watching the burden grow exponentially as enrollment redoubles; or he or
she can cut back and watch the quality of the teaching-learning process fall off in giving, by
necessity, fewer and fewer progress/incentive maintaining exams.

Avoiding these drastic alternatives is the foundation of the work behind this paper.
Admittedly, the computer isn't perfect; it is no substitute for good teaching by anyone's
estimation. But it may provide a very effective clerical substitute for the teacher, augmenting
his effective time and skills in this area.

Electronic computational capabilities allow us to get more out of teaching resources, which
may already be stretched beyond what is desirable or maintainable in the long run. If we are
particularly watchful of the pitfalls, responsive to the challenges, and aware that the computer
cannot do the whole job single handedly, much can be done to avoid a drastic stretching of
resources and/or lowering of educational quality.

In a deceptively simple statement, the goal we are working toward is to U3e computer
information processing technology to improve the cost-effectiveness of teaching basic
accounting, administering weekly progress examinations by a computer system. Prom non-classroom
and non-data processing experiences, here are operational aspects of how carrying out such a
compu ter /teaching system worked.

The Basic Computer System

Por each semester accounting course, large groups of questions for each week's materials
were collected. Generally graduate students in accounting were used to write questions utilizing
previous testing materials. These together with their approved answers, were placed in a
computer data base, then selected at random to create ten question examinations which were
printed out by the computer. These exams were numbered sequentially for each course and each
was given a grading code to be used as an input to the computerized grading and scoring program.

Each Monday night from 4 to 10 Pfl, students received a computer written exam paper and took
the exam by noting his course, name, student ID number, answers, and grading code onto machine
readable answer sheets. Keeping their questions (and having been instructed to indicate their
final answers on their questions) , students turned in their answer sheets, which were
electronically scanned and graded, the results recorded, printed up, and posted tor verification
by student ID number.

Introduction

ERIC

239

in order to provide prompt, adequate knowledge of results, the ten approved answers for
each exaa were printed up, and these were handed out by Batching with the exai nuaber as
students presented identification and turned in their conputer answer sheets. Thus it was not
necessary for students to surrender their questions and wonder about correct answers, nor did we
have to return their self-graded score with the conputer printed results that were posted.

Student Interface

The non-classrooB eleaents of student interface were the distributing of exans for each
course as students entered the exaa rooa, proctoring the exai roon (copying was out of the
question since each student had an individual fora of the exanination) , checking TO cards,
collecting and visually inspecting answer sheets for oversights, and handing out the correct
answers to natch each exaa. Although students could take as nuch tin*? as they wanted during the
exaa period, handing out the exans in sequence corresponded approxita tel y to the sequence of
answers needed on departure (with a few bottlenecks), and no najor confusions resulted while
this procedure was enployed.

Also, as the systen evolved, there was further student interface of najor iaportance in
regrading questions students wished to challenge, to Request for Credit (RC) forns. All phases,
except RC evaluations, could be handled entirely out of class by non-teaching staff.

Pcobjeas Encountered

The first problens encountered were in spacing and scheduling the exanination systen which
had served several hundred students within a fairly short interval of tine. At first, alnost
nobody showed up during neal hours, and the last hour produced explosive queueing problens. flany
of these nost obvious problens were self-correcting: after waiting forty-five ninutes, nany
students set out to arrive earlier or at less popular tines; furthernore, service rates improved
as students and staff becane nore faniliar with the procedures.

Cheating within the exaa roon was not a serious problen and nonitoriag was rarely
necessary. Occasionally partners would swap ex? Binations, although this was blatantly obvious to
students and nonitors alike and was a high risk strategy tried by very few. Controls could have
been instituted to insure that the sane exaa nunber and student nunber stayed together until
turned in, but this was thought to be costly and of dubious benefit under usual circunstances.

Cheating by sitting for one fora of the exan, turning in a defaced or blank answer sheet,
then retaking the exan with this knowledge was thought to be a ninor problen. As soon as
checkers learned, fron catching errors in copying or onissions, to exanine answer sheets at a
glance before accepting then, the opportunity for such "double-taking" by turning in an
ungradable answer sheet the first tine was extremely snail.

Occasionally an A201 student would take an A202 exan by Bistake. This did happen to a few
foreign students who passed blithely through the systen initating the fellow in front; however,
problens like this were rare and alnost always corrected before the student left the exanination
area.

Post-exanination queueing, milling about, and answer swapping proved to be the worst
initial problen. Having received their "approved" answers, to be conpared with their answers,
students frequently sat right down in the crowded hallway to coapare, exchange, visit with
students entering, argue out details, await for friends to finish, lanent, or celebrate. For
nany students to do this all at once, the burden on the tightly moving systen was too nuch,
encouraging extrene cases of prior "approved answer" exchanges and frequently preventing others
fron entering or leaving easily.

After six hours of collecting exans and approved answers fron the hands of friends, several
people developed their own data bank of questions and answers, as well as a good faailiarity
with the paraneters of the random selection progran selecting the questions. This problen also
exacerbated the difficulty of everybody showing up at the last ainute, having waited to collect
the news on all the tough questions in advance!

One could revise the exanination period, develop a question selection progran which
released only part of the questions into the selection pool for the exans to be given out
earliest, or institute harsher controls at various levels. However, senester schedules had been
established based on the 4-10 open exanination period and the burden of changeover would have
been quite undesirable.

Instead, the procedure was instituted to give out answers on the following day, fron 12 to
4 PH in a single roon. Large scale "data banking" during the exan was elininated; however, the
nore enterprising students with a strong working knowledge of the naterial in the first place

i H *

230

could still look up answers and, hopefully, improve their odds almost as
equivalent amount of time would have done!

luch as studying an

Passing out answers the following day led to its own facilities problems. Three tiles the
reasonably anticipated aiount of space was needed. There was considerable scattering once sheets
were stacked in groups of ten for self-selection of answers, it being impossible to hand answers
out individually under the circumstances. Student cooperation in restacking the scattered
answers helped alot, but often an angry student getting a bad grade left his stack of ten and
five others in shambles, undoing the care and efforts of many others.

Unfortunately, one would think students would remember their exam numbers or keep their
exam questions with then, but many did not. Confusion and poor communications in such a large
group were hard problems to overcome; a number of students didn’t really take the ten point
examinations very seriously; and other factors are examined below*

Distributing examination answers in one room for three courses saved amply on staff and on
confusion between designated pick-up points; however, this often led to picking up the right
numbered answers to the wrong course. Loud complaints about missing answers were resolved, as a
rule, by showing the student the pile for the correct course. On average, only one student per
week was unable to secure his answers during the distribution session after making judicious
efforts to find it. while a number of causes for missing answers was evident (friends picking up
friends* answers and so forth) X was aware of nobody who couldn*t find his answers after a day
or two.

It was discouragin
and take somebody else*
dropped by about 50%
improvement beyond that
classmates, wives, an
precisely where the app
forth (the placement
stopping by on her lunc
due to carelessness, pe

g that students continued to forget numbers, look in wrong course stacks,
s answers throughout the year. Although the frequency of such cases
between the first and second answer distributions, there was little
stage. The principal cause was that not students, but students* friends,
d so forth were picking up the answers for them. The student might know
ropriate answers were stacked, his course number, exam number, and so
of stacks was kept identical from week to week), but his girl friend
h hour hardly knew her way to the business building! Other losses were
rversity, and semi-sabotage, though all were quite minor.

We found that A200 had few enough sections that the answers could be sorted out by the
discussion section instructors themselves and given out at regular class meetings. This took a
major burden off of the confusion, as we were left with only two courses for which answers were
being self-selected. Unfortunately, students and their representatives, in dwindling but
persistent numbers, still showed up to get A200 answers five weeks after the changeover.

The situations in A200 can teach us much on several counts. In similar systems, one would
be wise to number A20 1 exams from 1-500, A202 from 501-1000, A200 from 1001-1500, since students
remembered cnly the exam number not the course when picking up the results for others. Even when
getting their own answers, students frequently didn’t notice the conspicuously placed course
number at the top of each page until they got home! Mutually exclusive numbering sequences would
prevent this confusion.

Furthermore, if one could carry out the large administrative and educational process
involved, differentiating discussion sections in handing out students* examinations would solve
many problems. For example, allowing Section #1 A202 students exams numbered 500-549 and Section

places for different

sections, (b)

distribution room

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Liminate altogether the need for a mass
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leeting. Depending on whether or not the

discussion sections
self-selection upon

could work out ways to
entering or leaving

Problems with Questions

Examination questions produced considerable trouble on many accounts. First of all, they
were not consistent as to directions because they were ordered at random. Using answer sheets
that allowed foe responses from A- Z or from 1*26, on question *1 a student might be asked to
mark "A” for true and **B" for false; on question #2 the same student would be told to write "T"
for true and HFM for false. Although there are pros and cons regarding severe penalties for not
following directions explicitly, equity required that students be given credit when confusions
of this nature were easy to make.

*41

231

Second, the best written objective question can often fee reed in two nays. The "one and
only one* correct answer, perfectly unambiguous to a person specialised in account j ;j at an
advanced level has a perfectly "correct" neaninq if looked at fron another point of view* at
tines, when read by a student specialising in mathematical logic, a question conld be
technically false or anbiguous, though to any accountant it was true. For example* "Debits
always equal credits in an accounting systen". .. but do they in the case of an undetected posting
error? In theory the two nust be equal: the answer is true. According to practice and strict
logic, there are occasional exceptions; the answer is false. •:

Third, there was every incentive to raise a conplaiat against a debatably anbiguous
question, as there was no penalty for an extrenely weak Bequest for Credit (1C) slip. Often the
stack was four inches thick at the end of a handing out session. A long, hard task of regrading
was required, judging each conplaint or coun terexanple on its own nerits.

Such regrading was fundanen tally unfair because one can hardly give points to all persons
answering the debits equal credits exanple question incorrectly, sone answering "B" instead of
"F" which the conputer accepted, sone having brought up the logical technicality justifying *F"4
and nany nissing it due to not knowing the naterial. On the other hand, onn can hardly throw out
the question and regrade all exaninations which (sonewhere) have that question, using a nine
point revised percentage scale. This is especially true whan the exception to the approved
answer is based on a special situation or well articulated technicality* . .which is the only way
the different answer could be justifiedl In recounting points, only those subnitting complaints
could be given credit for alternative answers, which gave a major incentive to submit BC slips
and exacerbated the problems in handling their large volume.

Fourth, many questions, being made by graduate students in accounting and/or with
substantial experience (indoctrination?) in accounting, tended to concentrate on fine
distinctions, which a basic accounting student night not grasp until he finished the year*s
work. Further, many questions asked almost the sane thing in a slightly different way (perhaps
an important one but nevertheless a confusing one). Complete consistency was impossible to
attain with nany question writers, and overlapping of similar points of theory led, at random,
to ample confusion and distraction.

Especially wben chapters assigned for the week covered a limited amount of naterial (for
example introductory chapters) one quickly reached diminishing returns on writing different
questions; yet the press of needing a large question pool to make the computer selection system
work invited fine distinctions rather than a few, well-worded, well-groomed objective questions.

Fifth, questions had a painful tendency to hinge upon a single word like "always," "never,"
"every," or "only" to make them unambiguously on^ of the alternative answers. This is a fact of
life with objective questions; however, it added to frustrations and complaints as students came
to realize and resent that an astute guesser could answer difficult questions without amy real
knowledge of the material.

Sixth, students soon came to realize that ten questions selected at random from a large
pool of hard and easy questions do not dependably measure one's performance on any single test.
The questions could easily all focus on one topic, or they could scatter over areas which were
not central to the readings. A large measure of chance cane into every exam, and the connection
between preparation and good performance was strained by the "luck/chance" factor. This is one
key reason why sone students did not take the examinations nor their results terribly seriously.
More questions per exam (this year there are fifteen per exam), mere consistency in the
questions, and better communications that o£ average students' preparation will be well measured
daring the tern are ways in which these problems can be remedied.

The computer teaching system achieved its major objectives, putting the computer to work in
what was formerly a high-cost, labor-intensive process of grading which was rapidly pricing
itself out of being a workable teaching tool. It is dubious that this amount of grading, which
was not itself faultless, could have been duplicated with the sane regularity and reliability
using traditional teaching methods, while emphatically not a sure-fire panacea, please renenbet
this qualification, conputer written and scored progress/iacenti ve exaninations can be quite
ef f ec tive.

In working with similar systems for educational needs elsewhere, one will find computer
systems like this one present a number of pitfalls which deserve planning and prompt remedial
attention. Many parts of our system proved to be far more labor-intensive than reasonably
anticipated; for exanple, evaluating the large number of answers challenged for good and bad
cause.

Contusions

232

flany iitqoitiflsf alienations, sad difficulties ii cosauaica tioss tended to arise, ud these,
««c« intensified by tbe conplexities of tbe sys tea. P rob lean sack as ticusivc ftC slips tsadsd
to go unchecked, sad a solatioa sack as reserving tbs right to penalise extra aely weak 1C slips
to bal an cs tbs incentives to subait tbsa requires careful planning, coanunication, aad
consistency in safoccsssat to as effective.

Givsa tbs outcry for aors effective usss of tsacbiag resources, ia assistiag tbs tsacbiag
process with high powered clerical services of coapatsr technology, ss fiad a asa as of inproving
the cost-ef fee Vi vs as ss of education. idaittsdly lsss tbsa perfect, sack a coapatsr systsa is a
better alternative tbaa either strstchiag tsacbiag rssoarcss by uasorkably 1 bo r- in tensive
axasinat ion procedures or reduciag the coaaitasat to frsgasat progres^/incentive aaiataiaiag
exaniaations.

i »

233

243

DIMINISHING SQUARES by Dorothy Holmes
Problem: Diminishing polygon forms with serial imagery

ERLC

\'A-<

£^^234

THE OSE OF A COBPOTBR FOE MOTI V ATI NG STODENT PROJECTS
IN UNDERGRADUATE COURSES ON NETWORK THEORY

Roland Priemer and Tadao Murata
University of Illinois - Chicago Circle
Chicago, Illinois 60680
Telephone: (312) 996-5491

ABSTRACT

This paper describes the use and content of a library of computer subroutines made
available to undergraduate students in courses on network analysis and network synthesis. The
primary concern in constructing this library was that it be organized to be versatile enough to
allow more originality and initiative in student projects than existing computer prograns for
network analysis and synthesis.

Introduction

This paper is concerned with a library of computer subroutines designed to motivate student
projects using a digital computer. Involved are students in a sequence of two senior level
courses on network analysis and network synthesis at the Uriversity of Illinois, Chicago Circle.
These courses naturally allow a meaningful application of t>e digital coaputer. The first course
presents the topological approach to network analysis. The second course is concerned with
various methods for designing networks from given network functions or desired network
performance. The prerequisite for these courses is a background in introductory circuit and
linear system theory. Also as part of the engineering core curriculum, all students have taken a
course on Fortran programming.

Incorporating the use of a coaputer in these courses has allowed the students to consider
more meaningful and practical problems. There are many conputer programs available tor both
network analysis and synthesis. Such programs are widely used in practice, and have become as
commonplace as the oscilloscope or the slide rule. However, most of these programs 3,re not
flexiole enough to be pedagogically useful in undergraduate courses on network theory. This
statement is bared on a number of observations (which are discussed in th: sequel) made by tne
authors and their students.

In addition to the use of the conputer, the authors also believe that the student greatly
benefits from working independently on long term projects. By allowing for a more active
participation in the learning process, a student*s involvement in an individual or small yroup
project helps to develop the initiative and self-reliance that he will be called upon to utilize
when he becomes a practicing engineer.

Observations on Motivating Prolec ts

Students at Chi^'^o Circle have been using the coaputer in the above mentioned courses
during the past several years. Indeed, almost all students have expressed a great desire to use
the computer.* This use has been in the form of students writing their own programs or using
large canned programs such as ECAP.

Students have expressed dissatisfaction with both of these approaches. Although students
have been able to write their own programs, this approach has received the most serious
criticism. This is due to the considerable amount of time required for writing and debugging
programs. The dissatisfaction with canned programs arises primarily because they are not useful
for understanding the theory on which these programs are based. Most students feel that neither
using canned programs nor writing their own in the time allowed contributes significantly to
understanding the techniques presented in these courses.*

The authors agree with a statement by Chua[3]that the use of a canned program Mtends to
create a strong student desire to depend heavily on canned automatic programs to solve even the
simplest of problems.* It was also found that canned programs do not motivate the student to
seek an understanding of the theory or the operations occuring within the computer, even though
these programs are used for dealing with practical problems. This reinforces the findings of
Dertouzos[ 5 ]•

♦ Student opinions are based on the results of questionnaires given to 120 students during the
last two years.

245

With the above considerations, the authors constructed a library of computer subroutines
based on the following guidelines.

1- The library should allow for a gradual increase in the use of the computer as the

courses develop and material is presented.

2. It should be possible to satisfy a student’s desire to participate in the programming
effort.

3. The interested and capable student should be able to develop his own specialized
programs by using the library as a basis or to augment the library.

4. It should be necessary for the student to use what he is learning in the course in
order to use the library of computer subroutines.

This libr :y has been used during the past year in the previously described courses.

Network Ana lys is Course Subroutine Library

Writing a program for the AC analysis of RLC networks is mostly an organizational problem
rather than a numerical one, and requires a considerable effort of the student. The subroutines
in the network analysis library represent the steps involved in applying the basic concepts to
solving problems. The subdivision of tasks allocated to each subroutine has been done in such a
way that the student cannot link together a set of subroutines to form an entire program unless
he understands the basic theory involved, with these routines, a student’s analysis program
consists entirely of a set of wCALLn statements, which, based on an understanding of the
concepts, h? must properly sequence. In the appendix is a list and explanation of these
rout ines.

For example, a studentfs loop current analysis program might be the following program.

COMPLEX VOLTS (30), AMPS(30)

DIMENSION X(100), Y(100)

CALL REDATA

CALL INCID

CALL RINCID

CALL TREE

CALL TIESET

DO 1 I 3 1,15

CALL BRACHZ

CALL ZLOOP

CALL EL00P

CALL I LOOP (AMPS, F)

CALL BCURR (AMPS, F)

CALL IBTOVB (VOLTS, F)

X(I) * F

1 Y(I) « REAL (VOLTS (3))

CALL PL0T(15,X,Y, 'HERTZbbb* , ’VOLTSbbb’, 'bbbbbbbbb
1 F ILTERbOtTTFinWOLTAGEbVSbFREQ . bbbbbbbbb r , r LOGb r )

END

In this main program, the student wanted a plot of the magnitude of the voltage across branch 3
as i.t varied with the 15 frequencies that were read in. In addition to this output, most
subroutines print out the results obtained within these routines. For example, ZLOOP prints out
the loop impedance matrix as a function of s.

Sir :c all information is transferred internally via common storage, the student can access
any of the variables in these routines by the addition of a few "COHUON" statements to his main
program. This will alio* considerable variations in the use of these subroutines. For example,
circuit information can be changed for a repeated analysis, any Fortran statements can be added
to the main program. This will allow considerable variations in the use of these subroutines.
For example, circuit intonation can be changed for a repeated analysis, any Fortran statements
can be added to the main program, or the student can develop his own subroutines for other
information. Also, any conceptually logical subset of these routines can be used to conform with
progress in the course. By the end of the network analysis course, students have written nodal,
loop, or node-pair analysis programs and are able to conpare the capabilities and limitations of
these different methods with respect to

— v a *

? ; i v>

numerical accuracy and computation time.

Net work S y p t fr e.s ji Coqr^e Subroutine Library

Reviewing past experience in guiding student projects in a network synthesis course* it
becomes evident that the originality of a student design project and the extent to which
projects are interesting and practically useful are greatly limited by numerical as well as
programing difficulties. Also, the time reguired for programing tasks which are actually
incidental to the insights sought in a project, restricts the types of projects students can
work on. These considerations indicate a need for programs in sole canned fora.

In opposition to the above conclusion stands the difficulty of determining what operations
these programs should perform. This problem arises because in a network synthesis course the
material that is presented consists of many specialized techniques, which are applicable only to
variously restricted problems.

The subroutines that are therefore in the synthesis course library can all be regarded as
utility programs, and thereby intentionally do not eliminate all the programming effort that
might be required of the student. Rather, some of these routines eliminate tedious numerical and
algebraic work, while others are the implementation of several numerical methods which may be
essential to student design projects. The subroutines in this library perform such operations
as:

Determine system functions of lumped, linear networks in symbolic form.

2. Obtain a partial fraction expansion of a rational function of s.

3. Calculate and plot the inverse Laplace transform of a rational function of s.

4. Obtain a frequency response. Bode plot, and Nyguist plot of a rational function of s.

5. Polynomial manipulation (addition, subtraction, multiplication, and division).

6. Evaluation of a polynomial from its zeros.

7. Function minimization.

8. Determine the roots of a polynomial.

In addition, each student whc, has taken me analysis course has written his o*n analysis program
allowing for synthesis by repeated analysis.

I mplementa t ion of the Library

At the start of each of the coulsgs previously described, each student receives a user
manual. The manuals explain the purpose and limitations of each subroutine and how the library
can be used. The library** is stored in on-line disk space.

For the first few weeks in the analysis course students are asked to call the subroutine
SAflPLE. This routine is an example of what might be a student's main program, and it enables the
student to become familiar with the computer center facilities. For the remaining part of the
quarter, each student is assigned a project. This involves the writing of analysis programs
using the library. These programs are then used, for example, to study the distortion due to
loss factors in reactive elements or to determine the power delivered to a network.

The subroutine library for the synthesis course does require the student to do some
programming. This adds a challenging factor to the projects assigned in the course. However,
this library attempts to eliminate the programming effort required for necessary operations
which are incidental to the insights sought in a project. Most projects involve a frequency or
time domain synthesis technique. However, some students have developed their own projects,
involving, for example, writing a program for obtaining system function in symbolic form using
topological formulas or doing a sensitivity study of some active networks.

** A listing of the library of subroutines is available upon request.

tXf t *

* 1

247

Conclusion

This library of subroutines was intended to encourage the student to discover foe himself
how the computer can be used to implement the theories presented in the previously described
courses. The authors therefore felt that it would be constructive to get sole student reactions
to the library. According to the questionnaire referred to earlier in the paper most students
agreed that the library provided a useful tool for integrating the techniques presented in the
courses and the use of the computer.

The authors believe that the library is helpful in three significant ways. Firstly* through
its use, the student acquires a better understanding of the capabilities and limitations of the
computer than through the use of canned programs. Secondly, the library described here requires
the student to apply algorithms to problems in a systematic manner. Finally* utilization of the
library allows the courses to be more independent project oriented such that projects are a
vehicle for implementing the theory and developing the student*s initiative.

ACKNOWLEDGEMENT

The authors wish to express their appreciation for the suggestions and comments offered by
their students, and for the contribution to testing and * deb uggi ng the programs made by A. C.
Petersen.

REFERENCES

1. Cosine Committee, "Some specifications for a computer-oriented first course in electrical
en qineer ing , M Commission on Engineering Education, Washington, D. C. * September 196tt.

2. N. Balabanian and T. A. Bickard, Electrical Network Theory. New York: John Wiley and Sons,
Inc., 1969.

3. L. 0. Chua, M A computer-oriented sophomore course on nonlinear circuit analysis*" IEEE
Trans, on Education* vol. E- 1 2 * no. 3, September* 1969.

4. J. L. Me Isa, Computer Programs For Computational Assistance In the Study of Linear Control
Iheory. New York: McGraw-Hill, Inc., 1 97 57

^ • Am L. Dertouzos, "Elements, systems* and computation: a five year experiment in combining

networks, digital systems, and numerical techniques in the first course," IEEE Trans. on-
Education, vol. E- 14, no. 4, Nov., 1971.

6- fl. 2 . Van Valkenhurg, Introduction To Modern Net work Synthesis. New York: John Wiley and
Sons, Inc., 1964. ~

P. M. Lin and G. E. Alderson, "SNAP-A computer program for generating symbolic network
functions, " TR-EE70-16* Purdue University, Lafayette, Indiana, August* 1970.

APPENDIX

"he following is
library.

Subroutine SAMPLE
Subroutine REDATA

The following routines a
Subroutine INCID
:>•* .{routine P INCID
Subroutine TREE
Subroutine TIESET
Subroutine CUTSET
Subroutine ZLOOP

a list and brief explanation of the subroutines in the analysis course

This is an example of an analysis program, which uses the library.

•This routine reads in the problem description, allocates informa-
tion in storage, and writes problem and output description.

re used for the topological analysis:

Obtains the complete incidence matrix of a graph.

Obtains the reduced incidence matrix ot a graph.

Finds a tree of a graph.

Determines the tieset set matrix.

Determines the cutset matrix.

Obtains the loop impedance matrix Z (S) .

t *

248

Subroutine

YNODE

Obtains

the

Subroutine

YDATUfl

Obtains

the

following routines are used for 1

the :

Subroutine

BRACHZ

Deteraines

Subroutine

BRACHY

Detemines

Subroutine

ELOOP

Ob ta in s

the

Subroutine

JNODE

Obtains

the

Subroutine

JDATUfl

Ob ta ins

the

Subroutine

ILOOP (AMPS,

Subroutine

VNODE (VOLTS,

Subroutine

V DATUM (VOLTS

, F)

Subroutine

BCURR (AMPS ,

Subroutine

BYOLT (VOLTS,

Subrou tin e

VBTOIB (AMPS,

Subroutine

IBT0V9 (VOLTS

, F)

Calculates the loop currents.

Calculates the node-pair voltages.

Calculates the nodal voltages.

Obtains branch currents froa loop currents.

Obtains branch voltages from node-pair
voltages.

Determines branch currents from branch
voltages.

Determines branch voltages froa branch
currents.

With the above routines, a frequency analysis can be performed using a loop, nodal, or node-pair
method* The following routines are support subroutines for the above routines.

Subroutine POL AH (A, N)
Subroutine LINEAH(A, N)

- Converts complex numbers from rectangular to
polar form.

- Converts complex numbers from polar to
rectangular form.

Subroutine PLOT (NPTS, X, Y , XUNIT, Y UNIT, - obtains a plot of the variables stored in Y
NAME, KEY) versus those stored in X.

249

ERIC

239

R COUISB XI COBFOTBI SIROLRTIOI RIB RIRLTSIS
FOR SCIIITISTS RID BR6IRBBRS

Brae* i. htiriw, Georg* l. Qoeetie end Rrther Hoeghtoe
The OeiTereitr ml lee lerico
Rlbeqoergae, lee lerico 87101

| Telephone: (SOS) 277-0509

1 mcfitagtiM

In this paper, n course currently being taught in the College of Bnginnnring at The

University of Bexico in described nnd discussed. The coornn in n one-seaester survey of

several of the large-scale analysis prograas cnrrnntly in ann throughout the conn try. The
coornn in orinntnd to n gnnnrnl nndinnen of stninntn f ron several disciplines sach ns Chnsicnl
Bnginnnring, flechasical Bnginnnring, and Vnclnnr Bnginnnring. It in taught by n tnaa of three
profnaaora of various dinciplinns in anpnrntn coatignona portions of tbn ananntnr.

The pnrticnlnr nnnlynin progrnaa atodind arn CSHP, Continuous Systna Modelling Prograa;
ECAF, Blnctronic Circuit Analysis Prograa; CIIDA, Chrysler laproved {fuser ical Diffnrnntinl

Analyser; CHBSS, Chnsicnl Bnginnnring Siaolation Systna; and COBFAC II, a coaputnr prograa for
tha dntnrainatioa of radiant intnrchaagn gnoantric fora factors. All students arn brinfly

introduced to nach of thnan prograas, and nach student is given an opportunity for aorn advanced
work with onn of tbn prograas by anana of a tnra project.

> afejgsUiti ot samt

The priaary dirnctioaal objectives of the DIB Collage of Engineering in teaching

j "coaputera" to its students can bn anaaariand aa follova:

1. To give the student a coaprnhnnsivn working knowledge of POBTBAB.

2. To tmeh the student the anthoda and uae of large "package" prograas.

3. To teach the student to take a prograa currently in use nlanvhere and aake it work on
the coaputnr ayatna he ia using.

The course ia intended to help fill part of the dnficinncina ia anaber two and, in soae cases,
nuabnr three. The need to introduce students to package prograas is eaphasized by the fact
that, aaong 20 nagiaenring profnaaora attending a recent engineering design seainar at Stanford,
only one, George Quentin, knew bow to use aay of the Continuous Syatea siaolation Languages,
even though they are siaple to uae and greatly enhance a person* a problea solving capability.
The courae is also intended to reach both students who are applications oriented and students
who are coaputer act once oriented and interested aore in aetboda than ia reaults.

There are a large nuaber of analysis progrnaa ia uae. Since it is iafeaaible to expose the
student to all of then, none croaa section of the available prograas aust be chosen. It is
desirable to let the atudent cospare the different progrnaa wit<« regard to the following:

1. Prograa types and potential use.

2. Bethoda of problea setap and data iaput.

3. Techniguea used in analysis.

A good way to choose prograas which have variety in the above three points is to choose both
general purpose progress, such aa CSBP, and apecial purpose prograas, such as CHBSS, as well as
to chooae progress froa various disciplines. Beeping the above in sind, the final decision to
teach a particular prograa can be based on the following criteria of a good prograe. The
priaary prerequisite ia that the prograa be available and convenient to the student so that he
can get several tara-arouada per week. This ia aost isportast to the learning process.
Secondly, the prograa should have a single input language which describes the problea structure,
states eleaeat or paraseter types aad values, specifies the excitations, and indicates the
analysis options desired. Third, it should be able to haadle nonlinearities. This is usually
done by either a piecewise linear approach or by \ aatheaatical aubroatine approach. Fourth, a
variety of output options should be available, such aa transient response, steady-state
response, plots, etc. Fifth, the prograa ahoald have the capability for autosatic paraseter
aodification with a solution being found for each paraseter value. Finally, the prograa aust
have self-contained error-checks aad diagnostics.

Few if any prograas will satisfy all of the above criteria. For instance, a special
purpose prograa aay not haadle a vide class of probless.

250

. . . .241

Based on the above criteria and the experience of the teaching professors, the progress
nased in the introduction were selected. The following section is a discussion of those
prograss.

Cba£§£te£i sties of t£e peggrass c^ojgn fg£ t|s SMI3fi

The S/360 Continuous Modeling Progrss (S/360 CSHP) is only one of a class of probles-
oriented prograss, or languages, designed to facilitate the sisulstios of costisuons processes
on large-scale digital cospnters (see Tsble 1). The class to which S/360 CSHP belongs is
referred to as continuous systes sisulstion languages (CSSL) following specifications set up is
1967 by the software cossittee of sisulation Councils, Inc. Prior to that tine, sajor computer
vendors each offered their own version of such a progras to run exclusively on their sachine.
The CSSL specifications have prevented divergence by selecting best qualities of several
available progress toward which vendors sight concentrate in future developsent. 1 langnage
called CSSL II has since been developed which closely follows the specifications snd runs on
several different vendors' large-scale sachines.

CSSL prograas are general-purpose tools primarily used in science and engineering fields
for the analysis of physical systess which say be described by ordinary differential equations.
These prograss are basically a set of functional blocks cosbined with a centralised nuserical
integration schese and a flexible language for cosnunication. They feature ease of progressing
with input statements capable of being prepared fros either block dlagras or differential
equation notation. The user say construct his own functional blocks, or Incorporate FORTRAN, to
tailor the progras for his own special purpose.

Consequently, typical applications have ranged fros sisulation of the husas cardiovascular
systes by physiologists to global ocean current sisulation by seteorologlsts. The universal
capabilities of the progras are in evidence in proceedings of the highly successful Susser
simulation Conference (Denver, 1970; Boston, 1971).

Because of these features, CSHP has been received by all students with overwhelming
acceptance. The student with sinisal computer knowledge quickly overcoses inhibitions as he
finds he can readily sodel a systes and achieve success with the program. The sore experienced
FORTRAN prograsser sarvels at the convenience CSHP affords, such as the provision for statesent
sorting to be done by the progras, and not required by the user.

The engineering student quickly adapts CSHP to aaay exasples fros his own field, using it

in his coursework or research. It has proven a boon to the instructor because the student
is more involved with physical system modeling and less with programming difficulties . Fur-
ther, the logic of users' simulation model can be easily scrutinized, which has proven -dif-
ficult with languages such as FORTRAN .

Teaching CSHP to a mixed group of students along with other types of applications prograss
has demonstrated the need for user-convenience in all such programs. This has been appreciated
by the engineer-user as well as the cosputer science sajor who say sose day assuse
responsibility for developing or saintaining sisilar systems.

The contrast of the general-purpose CSr^ with special-purpose applications prograas hss
emphasized the advantages and power of the forter. Limitations of tha special-purpose progras
are often frustrating, and the students find sodiflcation a formidable task. On the other hand,
if CSHP does not have the capabilities desired, it esn readily be cosbined with other
applications prograas. An exasple is cosbiaation of a CSHP sodel of an ethylene production
plant with a schese to detersine optimal design using the IBH Lisesr Progressing Package (HPS)
[ref. 2] . Another exasple is the developsent of the CHESS Progrss allowing it to generate CSHP
input statesents [ref. 3] . In this aanner, the blocks in the CHESS progras which represent a
steady-state chemical process say be examined in detail using CSHP to define their unsteady-
state characteristics.

Probless are assigned to demonstrate the facility of CSHP for sisulating systess resulting

TABLE 1. TYPICAL CSSL PROGRAMS

Nase

S/360 CSHP

Vendor

Int'l Business Hachines

IlSfelBS

IBB S/360

BIBIC

Int'l Business Machines

Control Data

Rand

Xerox Data Systess SDS Sigsa

7090, 7094
C DC 6400, 6600
Onivac 1106, 1107
Series

CSSL III

Prograssing Science Onivac 1108, IBH S/360

1. Hon-ltaear differential equations with variable coefficients (sea Fig. 1).

2. Sets of coupled non* linear differential equations.

3* Finite difference equations for the solation of distributed parameter problens.

For such problens, a naaerical approach is usually dictated, and CS!1P greatly shortens the
progransing effort.

In the cheaical industry, the design of chenical processes requires knowledge of overall
naterial and energy balances for a conplete plant project, A nunber of "flowsheet sinolator"
prograns have appeared in recent years to pronote conputer-aided design ventures, such as
General Electric Apache and Honsanto's Flowtran*

In such systens, a network of process equipnent nodules is constructed iu which physical or
chenical transf orna tions take place under the influence of variations in thernodynanic
paraneters. In the prograns, subroutines exist for various types of process equipnent. The
necessary physical paraneters are generated by appropriate correlations fron a library of
thernodynanic and transport properties.

The nathenatical problen inherent in nodels of such process systens is the required
solution of large sets of siaultaneou s, non-linear, algebraic equations.

The CHESS Chenical Engineering Sinulation System is currently available fron the University
of Houston at a noninjl fee. It is worthy of note that CHESS is not as powerful as other
connercially available prograns whose cost is indicative of their position in a competitive
narket.

A CHESS sinulation requires input infornation on feed streans to the process, structure of
the network, algorithns for each process nodule, and progran control paraneters. The progran
output contains (1) infornation on each interconnecting stress, such as tesperature, pressure,
heat content, fraction as vapor and chenical composition, and (2) calculated values of certain
equipnent design paraneters, e. g. energy required for a punp.

The value of a progran such as CHESS lies in the capability of generating Infornation for a
nunber of design cases, others have conbined optimization schemes and cost estinatiom packages
with these prograns. In this nanner, a nininal path search is nade for a set of optinal design
paraneters. The output then includes the cost infornation which is so vital to any engineering
design project.

The electronic circuit analysis progran, ECAP, is oriented toward electrical engineers, but
is by no neans United to problens in EE. nany problens in heat transfer, thermal radiation,
and nechanics, to nane just a few, have direct analogs in electronic circuits. ECAP can be used
to analyze these analogs. Since solution of problens by use of analogs is a widespread
approach, this is an inportant concept to teach the student.

ECAP uses a piecewise linear approach to the solution of non-linear problens. This is
sonewhat different than nost analysis prograns and offers a dranatic comparison to the student
when juxtaposed with the other prograns taught.

The input language of ECAP, which allows for the topological description of networks,
provides an inportant link with other circuit analysis prograns and is an easy-to-use method for
the student-user. Besides the input language, ECAP is divided into three convenient sections:
DC analysis, AC analysis, and transient analysis. This allows the stndent to quickly grasp the
basic progranning necessary. The user-oriented student can then advance to sore complex
techniques whereas the conputer science oriented student can concentrate on the techniques used
by ECAP.

ECAP has an automatic paraneter nodification feature which allows for variation of any of
the elenents in the DC and AC portions and for variation of frequency in the AC portion.
Modification is not allowed in the transient analysis portion.

There is also a self-contained error-check and diagnostic systen in ECAP which is a great
aid to the novice. Thus, it is seen that ECAP satisfies nany of the criteria for a good
analysis progran as defined in the preceding section and is, therefore, an appropriate language
to teach in this course.

The following is a sample problen which all students in the class are expected to solve
using ECAP:

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*• Determine the frequency response of the doablttiaid circuit s hows below for coupling
coefficient values of K*0. 3, 0.5, and 0.8 (M*=K >/Ll^2 ) . Plot the gain, VEi * i«
decibels and the phase shift, (@ - 9*) in degrees. Assune switch 1 is closed and

switch 2 is open.

b. Assaae both switches are open and c-j has an initial voltage of 10 volts. Deteraiae
the transient response e (t) , for the 5 psec period after switch 2 is closed. Ose
K30. 3. °

one of the basic objectives of the coarse is to provide faailiarisatioa with cenputer
techniques that are currently used in industry. Soae of these probless involve various
differencing nethods, the use of autoaated and conveaiently referenced iaforaatioa filing
systeas, and the interaction between complex sets of subroutines. In order to provide all of
these features and to allow the student to becoae faailiar with their utilization, the CIVDA
code has been chosen as a working tool. The fundaaeutal aatheaatics is easily described and the
stadent is led throagh one or two staple probleas before being requested to perfora a
preselected eleaentary solution. After that eleaentary solution has beea successfully
perforaed, the student is allowed to select a soaewhat aore complex aodel

A coaparison of the different types of physical probleas which aight be encountered allows
the student to see the total applicability of this type of differeatial equation solver. The
stadent is not required to obtain a detailed understanding of nil of the 350 subroutines which
are routinely available, but siaply east understand the basic analysis technique, the
rudiaentary flow diagraa, and the general philosophy of interconnection of the elenents. The
stadent is assisted in developing the ability to read the instruction annual and finally is
allowed to select a relatively large problea so that he can coaplete a solution which relates,
in a reasonable fashion, to the types of things that eaployers aight expect in the application
of aodern technology to the solution of real tine-varying scalar field probleas.

A aore Halted objective is chosen in the CORFAC analysis. This is a siaple numerical
aethod for deterain&tion of geoaetric radiant-interchange factors used in radiant heat transfer
and illumination engineering. The prograa chosen is not particularly aore appropriate that
other generalised analysis systeas, but the student is able to gaickly solve eleaentary probleas
of a general nature and can readily perceive the broad geoaetric inplicatioas of this analysis.
A siaple geoaetric problea is solved as an exnnple, and the stadent is enconraged to experiment
with the utilixation of the systea. A relatively brief aaount of tine is allocated to this
aethod since the generality is usually vested in the geonetric representation of the physical
problea.

Results

Responses of students taking the new course offering was good, judging froa the mount of
outside work which was accomplished. Host students atteapted to solve probleas using the
prograns (taught in the course) in conjunction with outside work. One exaaple was a stadent
taking a course in aodeling bioaedical systeas. After raaning a CSHP prograa froa the current
literature which siaulated the huaan temperature control systea [ref. 1) , he applied CSHP to
sinulate a auscle response aodel under discussion by his other class. Thu saccess of this
application sparked sufficient interest to warrant nn invitation to Dr. Quentin to speak to the
bioaedical class on CSHP.

Initial offerings uncover certain difficulties, and oar coarse vns no exception. In
assignnent of class periods aaong the three instructors, the senester was merely broken into
thirds. Bach instructor then taught consecutive periods until his aaterial was covered. This
proved not to be a convenience to the stadent who found it difficult to keep his program output
in pace with class discussion. This was not student failure as nacb as conpnter turn-around
difficulty. A related hindrance was that CIBDA was not running at the tise on The University of

ili

3rt

254

He* Bexico Computing Center IBB 360/67 computer. Consequently, italtit prograa flacks vara haad-
carried to oaa of tha local government laboratories vhara snchine tiaa vaa donated for reaming
CIVD A on a CDC 6600.

Oaa of tha banafita loat vaa that, by tha tiaa atadaata had achiavad a aoflaat laval of
undar standing of a prograa froa roaming a fav problaaa, tha aoabar of class period a davotad to
that prograa vaa coaplatad.

i student's capsule susnnry of tha programs offered ia gives belov:

CSHP a quick vay to computational relief and unsorted aadarataadiag

BCiP the electronics designer1 a computerized edition of "How to Analyze"

CIHDA a forward-backward nuaerical erector sat for hours of fun, profit and insanity

As discussed under resilta, the sequential aaaigaaest of class periods asoag iastractors
did not provide sufficient continuity for tha student. To renedy thin, it is planned, during
tha second offering, to assign one period par vaak (out of three) to each instructor. This
aeans running three programs in parallel. Students have pointed out that it ia feasible to keep
three different problaaa active simultaneously, thereby inproviag conpater turn-around.

The Engineering College has also been fortunate in obtaining aa IBB 1130 computer to serve
priaarily as a reaote batch terminal to the computing center IBB 360/67. This improves
input/output conditions for the college considerably since the computing center is none distance
away on the other side of campus. The 1130 computer also vill serve as a stand-alone conpater
during certain periods of the day as veil aa tines when the 360 is unavailable such as during
maintenance periods. v

A feature of the 1130 in the availability of an 1130/CSBP package, while this version of
CSBP is not aa extensive as the 360 version, it does provide interactive capability. Both
versions of CSBP vill be taught during the next offering of the course.

It was concluded that COVPAC and CHBSS vere probably too specialized and had input
languages which vere too structured to meet the objectives of the course. In the next offering,
these vill be replaced with VAST8AB (VASA Stress Analysis Prograa) and SCEPTVE (a program for
circuit and system analysis). There is no guarantee that this is the optinal selection. As
previously stated, there are aany possible' progress which could aeet the objectives. Sons
considered nost worthy by the authors are XCBS, 6PSS, GASP, and DIVABO.

while the course, aa described, has filled a void in the curriculum, it is considered by
the authors that the method used in teaching the course is nost meritorious. The authors have
visions of the course being offered at soae future tine as a simulation laboratory with the
individual student deciding which progress he wishes to study and how aany credit hours for
which he wishes to register. This would allow aaxiaua flexibility for students of any
orientation.

1. Vinton, H. J., and Linebarger, V. V«, Computer Simulation of Hunan Temperature Control,
Simulation J. , Vov. 1970.

2. tftsuai, T. , Stone and Vebster All-Purpose Simulator and Optimizer, and Its Applications,
Proceedings of Conference on Applications of Continuous System Simulation Languages, Sna
Francisco, July 1969.

3. Ingels, D. B., and Botard, 8. l. , A Process Dynamics Pre-Processor for CSBP, Proceedings of
Suaner Computer Simulation Conference, Denver, June, 1970.

4. IBB Systea/360 Continuous System Bodeling Prograa User's annual, wo. GH20-0367-3.

5. Botard, 8. L. , and Lee, H. B., CHBSS Chemical Bngineering Simulation Systes Oner's Guide,
Third Edition, University of Houston, Sept. 1971.

CHESS

COVPAC

handy self-taught programmed course in coordinate geometry for rotational and
translational freaks

less said the better

macs Elm

REFEREVCES

255

246

Ckryslar Corporation, Ckryaltr Iipronl laaarlcal Pl(f«rneU{ kulyttr for rklrd
Generation Coapntars, spaca olvlaloa Tackalcal iota TB-kP-t7-2B7, lav Orleans, oct. 1967.

Bougkton, *• *•» ■nd Bdeards, J., COIHC II, Tka IBB 310 version of a aaaaral Coapatar

Prograa for tka Oataralaatloa of Radlaat Xatarckaaga Oaonatrlc Porn factors. Back. Baer.
Dapt., 0ni». of Be* Baxlco, klbagaargaa, Jaa. 1971.

Jansen, a. a. , and Lleberaaan, B., IBB Blactroalc circalt analysis Prograa, Praatlca^Ball,

«5e

247

REALIZATION AND CLASSBOOfl APPLICATION Of A DISPLAY
BASED SYSTEA FOB A SHALL DIGITAL COHPOTEB

Donald C. Aaoss and John N. Gowdy
Gleason University
Gleason, South Carolina 29631
Telephone: (8Q3) 656-3379

Introduction

An Lntorductory course in the computer sciences should include such topics as logical
structure of digital systems, aachine organization, inforaation flow, data transfers,
coanunicati on with external devices, and interrelationships between hardware and software.
Typically, such a course aust deal heavily with aachine and asseably codes to the point where
sufficient proficiency is achieved to allow deaonstration of the other points mentioned. Several
approaches could be taken, each with its inherent advantages and disadvantages. A hypothetical
language could be used, designed optiaally for the course being taught, but this elininates any
possibility of what is learned being directly applicable to any real world conputer and, in
addition, usually inspires little enthusiasa ia the students. To use a large machine's asseably
code would be very difficult because of the extensive instruction set and the probleas that
often develop when running poorly written aachine code prograas on a large systea atteapting to
handle these jobs in the noraal job stream. Therefore, it would seen that a real, snail conputer
asseably language would be nearly ideal for such a course. However, there are still at least
two alternatives. A siaulator for the snail aachine could be run on a large aachine with noraal
progran subaittal procedures as with higher level languages. There are certainly distinct
advantages to this approach when dealing with large nunbers of students; in fact, large enough
numbers nay preclude any other approach. However, eventually the students1 approach to problen
solving for this course would becoae identical to courses dealing with higher level languages;
only the language would be different. There is a lot to be learned when forced to "run" your own
coaputer that is not appreciated by those who subait a deck of cards and inpatiently wait for
the neatly folded answers. It is, perhaps, particularly iaportant for future electrical
engineers to have literally "hands on" experience with the collection of electronic circuits
called a digital coaputer* This opportunity is enthusiastically embraced by aost students.

If the decision is aade that "hands on," real use of a snail coaputer is an iaportant
feature to be included in the coaputer portion of an electrical engineer's education, then the
question arises as to what can be done to optimize his experience without excessive cost or
total investment. Any attempt to use punched paper tape as the only bulk storage aediua would
meet with immediate failure. On the PDP-0, one coaplete cycle of editing, asseably, and test
execution with the required loading of the editor, asseabler, and user progran (the latter,
several tines per cycle) requires approxinately one hour. (This is obviously dependent on user
progran length, but loading the editor and assembler requires over 30 ainutes.) Sone other fora
of bulk storage such as magnetic tape or disk is obviously necessary. Magnetic tape is less
expensive and allows students to keep their own prograas and jperating systea if they so desire.
The system to be described uses nagnetic tape bulk storage. Sone coanents should be aade
regarding existing systems for this coaputer using nagnetic tape. Perhaps the aost iaportant
criticism of existing systems is that they are not a systea, but rather one progran with a
directory for calling all other prograas including the asseabler and editor. Since each prograa
is handled independently, no internal intercoaaunicatioa exists, and file nanes aust be
specified to every program called. Since the students will not require the greater flexibility
possible with such an arrangement, there is no advantage for then. To the contrary, since the
students will almost exclusively be working on one user progran at a tine and repetitively
calling the editor, assembler, and loader, it would be less convenient and slower. The asseabler
should assume the program in the editor is the one to be assembled. When finished it should
recall the editor with the sane program already there either for aodification and correction, or
loading and execution.

The other major problem encountered on snail computers *s the usual output device- the
teletype. Although the need for the teletype was not eliminated in the systea to be described, a
large portion of the intermediate use has been eliminated and replaced with a display scope. The
only major time consuming task remaining is the listing of programs. Some thought is presently
being made with regard to this problem and the possible addition of the line printer capability
to eliminate this problen. Of course, the total investment for a coaplete installation would be
significantly increased.

Systea Description

Based upon these primary objectives, SCPSYS (SCoPe SYStea) was written. The result was an
interactive CHT/keyboard operating systea capable of quick user response in performing editing.

249

257

asseabling, and filing on a 4K, 12 bit word POP- 8 computer. The systea's capabilities caa be
alaost completely suaaarized by the command set. A brief description of these coaaaads' will
follow a description of a few of the fundaaental features of the systea. All input is via the
teletype keyboard or reader. Once the systea is loaded, all operations can be perforaed via the
keyboard with the exception of aounting different tapes, user prograa halts, tape hardware
aalf unctions, etc. That is, the systea does not use the switch register or an; other isput
during its noraal operation; SCPS7S does not use the interrupt. The pritary output device is an
oscilloscope. (Our systea has a 1 2" x 12” X-T scope, but any oscilloscope of fast enough
response tine (10 RHZ) and with Z-axis aodulation should be adequate.) The teletype output echo
can be suppressed (see coaaands listed later). The systea has within it working areas for the
current manuscript or source prograa and the current binary or object prograa. Hheaever the
systea is called (or recalled) it displays the last several lines of the aanuscript working
area. (The actual nuaber of lines displayed is adjustable by the operator.) Any portion of the
aanuscript working area can be displayed through proper use of the conaands. All editing *s
perforaed with regard to what is being displayed. nothing can be deleted froa the working area
that is not being displayed. The display output is auch aore rapid than the teletype oriented
editors so students can "see" aore of their prograa without excessive tiae consumption. This
greatly increases the user's confidence in what he is doing to his prograa.

The minimum hardware configuration for using SCPSTS is a PDP-8 coaputer with:

1. 4096-word, 12-bit core aeaory

2. Extended Arithaetic Eleaent (EAE)

3. TC01 DEC-tape control

4. One TU 55 magnetic tape transport

5. Two digital-to-analog converters and buffers (D/A)

6. CRT with appropriate amplifiers for D/.t

7. ASR33 Teletype

It should be noted that SCPSYS operates aore efficiently with two (or aore) T055 tape units, but
only one is required. The estiaated cost for a ainiaal systea configuration is S14,000. It nay
be advisable to acquire a systea with a aore flexible aagnetic tape controller for an estiaated
$21,000.

SCPSYS is stored on a standard DEC-tape and is loaded into the coaputer in the sane Banner
as other DEC-tape oriented systeas. The systea occupies approxiaatel y 22% of the tape with the
remainder available for user prograas. If a second transport is available a file tape can be
mounted on it which has over 99% of its space available for user prograas. The index provides
file oriented storage for aanuscript (source) and binary (object) prograas of the saae or
different names (eight character file identifiers.)

To perform functions within the operating systea, a set of "executive coaaands”has been
established. All other keyboard reader input is assuaed to be new aanuscript to be added to the
existing working area aanuscript. These coaaands are requested by starting a new line with a
special character (>) which causes the rest of that line to be displayed (preceded by an
arrow, •>) at the bottoa of the screen. A two character code is used to identify the desired
action to be taken followed by any required paraaeters. A convenient set of default conditions
exists which provide a aeans for rapidly asseabling and executing prograas during the debugging
stages; no filing is necessary until desired.

To complete the discussion of the systea features, each of the available coaaands will be
briefly descicbed. The commands can be divided into three categories; editing, filing, and
assembly and execution.

The editor is the central prograa in SCPSYS in that all other operations are initiated froa
within the editor. It is capable of handling nearly 50,000 characters (aore than sufficient for
student use) with no provisions for handling larger prograas in aanuscript fora. The aanuscript
is entered via the teletype after which it can be aodified by adding or deleting characters,
lines, or large segments with the aid of the following coaaands.

1. Line calls: A request to aake a specified line the current display line so that soae

editing operation can be perforaed. Fjr fine adjustaent, a sequence of two characters
is used to reposition the display backward or forward a line or a fraae at a tine. (A
fraae is equal to the nuaber of lines being displayed; usually six.)

Add Manuscript: A request to add a manuscript previously filed by SCPSYS to the
working area. The aanuscript is added at the location in the working area at the tiae
the command is given; beginning, middle, or end.

Editing

250

3. Print Aanuscript: A request to list the contents of the working area or a specified

■anuscript file. Portions of aanuscripts nay also be listed by specifying desired
range of line nunbers.

4. Erase Aanuscript: A reguest to erase a portion or all of the working aanuscript area.
Display can be anywhere within the working area when this coaaand is given. A single
line can be erased by requesting that line to be displayed and typing RUBOUT.

5. Search for Character String: A request to locate a specified character string

(United to eight characters) within the working aanuscript area. Since tagged lines
are usually preceded by the synbol for indenting purposes (see discussion of
assenbling), the search can be United to tagged variables or unrestricted to any use
of the string.

6. Character Editor: A request to perforn single character aodif ications within the last
line being displayed. When the desired location within the lines is reached* erasing
or adding characters is on a one character at a tine basis. No editing takes place
that is not visible on the display; i.e.* only characters displayed can be erased and
insertion of a new character is innediately displayed.

7. Display Syabols: A request to display the alphabetized list of the synbol table of

the last program as sea bled. This aids in the debugging stages to confirn that a new
symbol to be use is not currently in use.

8. Set Display Lines: Adjusts the lines per frane to the value indicated.

9. Disable Typing Echo: A request to eliminate echo of teletype input. Particnlarly
advantageous when inputting programs fron punched tape.

10. Enable Typing Echo: A request to provide echo of teletype input.

11. Select Character size: A request to set size of characters in display. Of sone value
during demonstrations to provide larger* nore readable characters.

1. Save Aanuscript: A request to create a file and store the contents of the working

aanuscript area as a separate user file.

2. Save Binary: A reguest to create a file and store the contents of the working binary
area (object programs) as a separate user file.

3. Copy Aanuscript: A request to transfer a aanuscript file fron one tape to another.

4. Copy Binary: A request to transfer a binary file fron one tape to another.

5. Display Index: A reguest to display index of prograns file on indicated tape.

Prograas (either binary or aanuscript) nay be deleted at this tine but two separate
and deliberate acts are required.

6. Print index: A request to print (hardcopy) index of prograas filed on indicated tape.
Sone additional inforaation is also typed with regard to filing space still available
on tape.

7. Create Index: A reguest to initialize a new index on a tape that does not have one.
Asseabling

Aside fron a few features to be discussed below# the asseabler is the sate as PAL III
Syabolic Assembler (8-3-5). A "text node1* has been added to provide a convenient weans to store
character strings for user prograa output. As aentioned above, the character ”t” at the
beginning of a line is not "seen" by the asseabler but is used in all output, both display and
hard copy, to provide indenting for easier reading of prograa listings.

1. Convert: A request to asseable specified aanuscript (Passes 1 £ 2 of PAL III

asseabler). Resulting binary (object } prograa is stored in the binary working area.
An alphabetized synbol table is displayed upon conpletion.

2. List: A request to provida a complete assenbly listing ot specified aanuscript

(Passes 1 6 3 of PAL III asseabler). Listing usually begins with the synbol table but
it can be deleted.

zs<j

251

3. Add Binary: A reguest to concatenate a filed binary prograa with the binary working

area leaving the result in the working area. This provides an easy Beans tor
overlaying prograns, or adding subroutines or data to user programs. m

4. Load Binary Prograa: A request to load and execute a specified binary prograa. All

of memory, except the bootstrap area, can be loaded via this coaaand. Starting

address can be specified at load tiae, defaulted to 200, or taken froa index as the
value specified when prograa was filed.

5. Exit: A request to store existing status on tape and put all loaders in aenory ready

for the next user.

6. User Defined Commands: A request to perfora soae user defined coaaand. The coaaand
"7f" causes the system to load and execute four blocks of user written prograa
which can branch on the contents of the accuaulator which is set equal to the
character after P in the coaaand. This provides soae flexibility in nodifying the
systea and adding functions often used by specific installations.

In addition to the main systea just described, there are several auxiliary prograns which
make use of the display based features to provide several user required functions. They
include: a b lock- to-bl ock DEC-tape copying prograa; a prograa to list the octal contents of any

DEC-tape block; a prograa to aodify the contents of any location on any DEC-tape block; a

program to translate "DECUS" manuscripts to SCPSYS aanuscripts; and DEC-tape read/write

subroutines within the bootstrap loader area always available for user prograns.

Classroom Application

The course in which SCPSYS was used was Electrical and Computer Engineering 350 at Cleason
University. Two sections of the course were taught, one with fifteen and the other with sixteen
students. The catalogue description of the course is given below:

E 5 CE 350 Principles of Digital Conputer Systeis 3 credits (2, 2)

Introduction to machine structure and progiaaming systems. Topics include: general aachine
organization, information flow within a aachine, internal and external data types and
structures; data transfers and communication with external devices and interrelation
between software and hardware. The various levels of programing systeas are considered,
but the main emphasis is place on aachine languages. Prerequisite: Approval of department.

Although this is a junior-senior level course, it was assumed that students had no prior
background in computer organization and assembler language programming. This was a three credit
hour course, consisting of two one-hour lectures and a two-hour "workshop” period which could be
used at the instructor's discretion for either a laboratory period or for an additional lecture.

The main text for the course was Computer Organization and Prograaai ng. by C. William Gear.
The prescribed text proved reasonably satisfactory and was followed fairly closely for about a
month duriug which the basic concepts of the course were introduced. However, because of the
availability of the PDP-8 computer, it was decided to base a large part or the course on
homework assignments to be programmed on this machine. The availability of SCPSYS as a
programming aid contributed significantly to the decision to use this approach. In particular,
it was felt that SCPSYS would allow the student to interact with the computer at a basic level,
without the tedious task of using numerous paper tapes to realize system software.

The process of familiarizing students with SCPSYS was begun with a thorough demonstration
of system utilization. After the capabilities of the system had been deaoustra ted, each student
was given a comprehensive manual describing in detail the different aspects of the system and
their use. Then successively more difficult homework problems were assigned to be worked using
SCPSYS on the PDP-8. The first assignments were taken from Introduction lo Prograam ing published
by Digital Equipment Corporation. Many aspects of assembly language programming were included,
such as subroutines, I/O programming, and interrupt programming. The final assignment involved
determining the sample mean and variance of a block of 100 stored data words. This assignment
required knowledge of normalizing, scaling, exponent formation, and I/O operations, in addition
to basic arithmetic and control programming.

Although the PDP-8 computer was generally available for course use, it did have other
commitments. For this reason the following regulations were established for system usage:

1. Two hours were reserved each weekday for class use. Students could sign up in advance
for single hours of computer time during these 2-hour periods.

252

2. Students could use the computer at any other time when it was not busy,, One hour was
the maximum time any student could use the machine it there were other students
wai ting.

3. Several students working together could sign up for longer blocks of computer time it
needed. However, individual work was strongly encouraged if time permitted. students,
were allowed to use the system during evenings, weekends, and holidays, whenever
possible.

From the instructor's point of view, the major advantages of SCPSYS as a teaching aid were:

1. Ease with whrch students would call, edit, and restore manuscript programs. In

particular, th< ability to "see" changes as they were made contributed to the
r* J ent's development of confidence in interacting with the computer.

2. Ease of assembling and loading programs for execution.

3. Ability of the system to hold a student's interest on fairly complex homework

assignments inv ''ving assembler language programming. Almost all students exhibited
some degree of Luscination with the system, and this attitude undoubtedly contributed
to their motivation and perseverance in completing the homework assignmen •

Although overall educational effectiveness of SCPSYS was very good, several disadvantages
were noted. These are discussed below, along with proposed methods for overcoming them.

1. The abiLity for a careless or erratic student to "bomb” the DEC-tape containing

SCPSYS as well as other students' filed programs was a principal disadvantage. This

vas due in part to the impract ica lity of having a supervisor present at all times.

This problem could essentially be eliminated by requiring each student or small group
of students to purchase DEC-tapes.

2. The length of time required to obtain hard copy of stored programs was another
problem. Especially for large programs, the inordinately long time required to obtain
a listing from the teletype resulted in inefficient use of the computer. One Way to
eliminate this problem would be to add a small line printer to the system. In fact, a
printer of some sort is almost essential if moderately long programs are to be
assigned to a large class. However, this will require an additional investment of an
estimated $7,000.

In order to obtain student reaction to using SCPSYS, a questionnaire was prepared and

distributed to the class at the termination of the course. This questionnaire consisted mostly

of specific questions related to the system, but also included questions by which students were
asked to express any opinions, favorable or unfavorable, about SCPSYS. The findings of the
questionnaire are summarized below.

In order to consider the results in proper perspective, students were first asked to
indicate any previous experience in machine language or assembler language programming. About
17% indicated some previous experience. The average time of system usage for students working
alone was 1.8 sessions/week with 1.7 hours/session. Also, each student averaged .8 session/week
with .8 hour/session working in a group. This indicated a total average of J.b hours/week, it
is felt that this estimate is high, due to the fact that the questionnaire was distributed at
the end of the course when many students were spending considerable computer time completing
work which should have been finished much earlier in the semester.

One of the most important questions that arises from using SCPSYS in a cooputer course is
whether the time required to become proficient with the system is worth the benefits gained from
using the system. Ninety-two percent indicated that they felt that the time spent to learn the
system was worthwhile. Also, the average time to learn how to use SCPSYS was 2.7 hours.

{lost students listed the capability of editing with visual ail as the principal system
advantage. Other advantages listed were • wide variety of system commands, quickness of system
response, fast checking of manuscript programs, and general ease of executing programs.

Host system disadvantages listed by students were related to the slowness of the teletype
in producing listings. This not only prolonged the time required of each student to complete his
homework, but also caused sigrificant waiting times for other students who needed to use the
machine. Some students complained about having their filed programs accidentally destroyed by
othjr users.

Overall, most students indicated a fairly strong approval of SCPSYS as an educational aid.
In fact, 96% indicated that the use of SCPSYS made the homework more enjoyable, and 88% said
that the course as a whole was more enjoyable due to tbe use of this system.

261

Conclusions

SCPSYS, a scope-based systea for editing, filing, asseabling, and executing programs on a
4K PDP-8 coaputer9 has been used in our introductory course in coaputer organisation and
prograaaing in the Oepartaent of Electrical and Coaputer Engineering at Clenson University. It
has been found that this systea not only pernits the coaputer to be used aore efficiently, but
also that it is conducive to the developnent of a high degree of aan-aachine interface. A
student questionnaire strongly supported these conclusions. Students were able to becone
proficient with SCPSYS in a short tine, and felt that the tine required to learn the systea
“as well worth the advantages the syctea provided. Because of these overall advantages provided
by SCPSYS, d "hands-on* experience on a real digital coaputer was provided in this course to a
significant nunber of students. In suaaary, it was generally felt that SC?STS contributed
appreciably to the overall effectiveness of this introductory coaputer course.

REFERENCES

Gear, C. Williaa: coaputer Organization and Prograaaing: BcGraw-Hill; New Tort, 1969.

Introduction to Prograaaing: Digital Equipaent Corporation; Maynard, Bass., 1970.

Lovell, Bernard W.: A Simulated Hini-Conputer Package to Teach Introductory Machine and

Assembler Language Programing; Purdue 2211 Sya. on Appl. of Coap. to Electr. Engc. Edge.:
Purdue University; Lafayette, Indiana; April 26-28, 1971. *

Burger, Peter: A Teaching Oriented Systea for a Hini-Coaputer ; Purdue 1971 §ya. oji Appj.

Coojd. to Electr. Enqr. Educ. ; Purdue University; Lafayette, Indiana; April 26-287 1971.

COMPUTED- ASSISTED NUMERICAL CONTROL PART PROGRAMMING

Paul T. Moriarty
New Torn City Community College
Voorhees Campus
New York, New York 10036
Telephone ? (212) 563-1370

I nt roduc t ion

In Spnny 1971, Voorheas Technical Institute (now the Voorhees Campus ot New York City
Community College) offered two courses in Numerical Control (N/C) in the Evening Division. The
first course, MT 420 (Tabla 1), dealt specifically with the manual part programming of a
drilling and Billing machine. Its objectives were to familiarize the students with the
principles and theory of N/C, and to give them hands-on experience in the machining ot parts by
numerical control.

The second course in the sequence, MT 440 (Table 2), had as its objectives, giving the
student an exposure to computers and showing them the benefits ot computer-assisted N/C, through
actual hands-on use ot a computer in part programming.

Har dw ar e and Facilities

The Machine Tool Technology laboratory has a Bridgeport J-axis miller with a Slo-Syn
Control Unit, along with a Friden Flexowriter for manual tape preparation and all the tooling
necessary to maintain the courses. The Computer Science laboratory is equipped with an IBM 1130
3 K CPU, card read/punch, line printer, disk drive, plotter, and paper tape I/O along with six
key punches.

I was contacted in October 1970 regarding the Machine Tool Departments desire to interface
the two departments and to develop the MT 440 N/C course. I assumed responsibility for this
interdisciplinary project. It was obvious that I had to guickly learn at least the following:
what is involved in numerical control machining and how computer-assist is presently used and
the details and operations of both the Bridgeport miller and Slo-Syn Control unit.

To prepare for the study which followed, I had conferences with the machine tool staff and
observed laboratory sessions, I visited the Superior Electric Company, manufacturers of the Slo-
Syn system and the Bridgeport Machine Tool Company? I attended the MT 420 course and ob-
tained all the literature readily available concerning computer-assisted N/C.

IkS Approach

One of the course objectives was to give students entire hands-on experience in the use of
the computer. Gradual exposure, through the practical application of the computer in increasing
degrees of complexity allowed the student to advance slowly to full utilization ot hardware and
software available tor numerical control. This success was accomplished through tne simplified
design of the software, atd having hardware that encourages hands-on usage.

Another objective was to have students program parts with geometric patterns, tedious to do
by hand, but made relatively simple with computer-assist. The students* first manual part
programming assignment gave them an understanding or the difficulty of advanced programming, and
with the use of the computer they were able to program a final part which would nave been nearly
impossible to do manually.

The Software Design

Goon alter acquiring enough information about the N/C equipment and programming, I began to
search tor 1130 N/C software. Although there are two Type IV programs in the IBM 1130 Catalog ot
Programs, neither had a postprocessor for the Slo-Syn system. Tnerefore. I decided to develop
"customized" software tailored specifically to the hardware available. Many restraints wore
considered in the software design: the programs had to be written quickly and with minimum

MT420 BASIC NUMERICAL CONTROL (N/C) MACHINING COURSE
2 EVENINGS PER WEEK, 3 HOUR SESSIONS 7*5 WEEKS (45 HOURS)

TOPICAL OUTLINE

INTRODUCTION

IV.

USE

OF FLEXCWRITER

TYPE OF N/C SYSTEMS

SET-UP OF MACHINE

* •

REFERENCE POINT SYSTEMS

TAB SETTINGS

TAPE FORMATS

CORRECTING ERRORS

FILM

REPRODUCING TAPES

II.

THE

SLO-SYN SYSTEMS

PROBLEMS

THE SLO-SYN MCU CONTROLS

DRILLING ONLY

THE BRIDGEPORT CONTROLS

MILLING ONLY

SPINDLE-WIZARD CONTROLS

DRILL/MILL COMBINED

DEMONSTRATION

Z-AXIS PROGRAMMING

ROTARY TABLE PROGRAMMING

III.

PROGRAM WRITING

POINT-TO-POINT

VI.

INTERPOLATION

CODING SHEETS

CIRCULAR AND LINEAR

TAPE FORMATS

POINT-TO-POINT ARCS

MISCELLAEOUS FUNCTIONS

CONTINUOUS PATH *

DRILLING DEMONSTRATION

PROGRAMMING

CONTOURING PROGRAMMING

Table 1

MT440 BASIC COMPUTER-ASSISTED NUMERICAL CONTROL
2 EVENINGS PER WEEK, 4 HOUR SESSIONS 7 *5 WEEKS (60 HOURS)

TOPICAL OUTLINE

I. REVIEW OP N/C

1 . TAPE FORMATS

2 . N/C CONTROLS

3 . COORDINATES

4. MANUAL PROGRAMMING

5 . BOLT-HOLE-CIRCLE PROGRAM

V. MACHINE TOOL LABORATORY

1. REVIEW OF CONTROLS

2 . DRILLING BOLT-HOLE-
CIRCLE

3. REVIEW OF TOOL
CHANGES

II. INTRODUCTION TO COMPUTERS

1 . COMPUTER SYSTEM

2. COMPUTERS IN N/C

3. PUNCHED CARDS AND OTHER MEDIA

4. DEMONSTRATION OF SSNCS AND
COMPUTER UNITS

III. PREPARATION OF COMPUTER INPUT

1. CARD COLUMNS, FIELDS

2. USING THE KEYPUNCH

3. SSNCS CODING SHEET

4. KEYPUNCHING BOLT-HOLE-CIRCLE

IV. COMPUTER LABORATORY

1 . SLO-SYN PROGRAM

2 . KEYPUNCHING DATA

3. INPUT TO SSNCS

4. TAPE LAYOUT FROM SSNCS

VI. IDLER-PLATE DRIVE LINK

1. USE OF SSMAC

2. CENTER DRILLING ONLY

3. USE OF SSNCS

4. ANALYSIS OF OUTPUT
FROM SSNCS

5. HOW TO DEBUG PROGRAMS

VII. MILLING OPERATION

1. RESULTS OF EXPERI-
MENTATION

2. ACCURACY OF SSMAC

3. TOOL CHANGES AND
PROGRAM MODIFICATION

VIII. TOTAL COMPUTER ASSIST

1. CARDS FROM SSMAC

2. MERGING CARD DECKS

3. ACCURACY OF PLOTTER

4. DEBUGGING AND ERRORS

IX. MACHINE TOOL LABORATORY

1. MILL/DRILL CONSIDERATIONS

2. MACHINING OF FINAL PART

Table 2

i .

264*56

testing, due to the lack of t^ie; extensive error-checking and diagnostics were necessary in a
student environment; and most important - the system aust be interactive with the student to
facilitate hands-on usage. The software written was named SSNCS/113G - Slo-Syn Numerical Control
5yst2m/IBM 1230; Figure 1 is an overall flowchart of the system, and more important features are
listed in Table 3.

For geometric part programming, a separate system was designed, based on Digital Equipment
Corporation's "Uuickpoint - 8" N/C system. An interested senior computer science student was
assigned the task of writing the programs as a term project for one of his courses. The system
implemented was labelled SSrtAC - Slo-Syn HACros. The term "macros" was chosen since the programs
would generate many data blocks from the one line of parameters input to them. The SSflAC system
interfaces with SSNCS by punching the data blocks into cards in the format required by SSNCS.
The patterns provided by SSMAI are: Bolt hole circle (BHC) ; line at an angle (LAA) ; grid (GRD) ;
increment along a line (INC); and points along an arc (ARC). It would have been more desirable
to have the macro commands as part of SSNCS itself, but time did not Permit their incorporation
into the system. It is expected that this may be done later.

Because of the haste with which SSNCS and SSMAC were written and the lack of time for
complete testing, students were advised to report any problems or errors they thought they had
found. As errors occurred, aa error log was kept, and they were corrected as soon as possible.
Fortunately, all errors discovared were minor, and corrected by the next meeting of the class.
Suggested improvement and modifications were done quickly if of a minor nature, but major
modifications were logged for future incorporation.

Course Assignments

The part programs done by the students were structured so that each assignment required the
student to grasp new concepts p iece- by- piece and to allow him to use the concepts in practice
before advancing to new material.

The first assignment was the complete manual calculation, programming and tape preparation
tor a nine-hole bol t- hole-ci rcle . This gave the student a realization of the difficulty of
geometric calculations and a review of manual part programming. Having done this, the next step
was the use of the computer in doing the calculations, yet stiLl requiring the manual tape
preparation. A program in the Slo-Syn Handbook was used, which read one data card containing
the parameters for the circle, calculated, and printed the X and T coordinates. The student was
instructed as to the use of the keypunch for preparation of the parameter card and two control
cards for executing the program. In the computer lab they were guided as to the operation of the
computer and what buttous to push. Since it was their first experience at the consoles, the task
was simple enough to ue mastered quickly, giving them a sense of accomplishment, and an easy
familiarity with the computer system. The programmed bolt-hole-circle was then machined in the
N/C laboratory, providing students with a review of the controls and operations of the Slo-Syn
system.

The next part to be dole (Figure 2) was taken from an IBM N/C Course Instructor's guide.
With this part the student would learn and use the SSHAC and SSNCS systems, along with all the
computing hardware. The first step was the center-drilling of all holes, and SSHAC was used for
calculation of the two bolt-hole-circles. The cards from SSMAC, along with the manual
programming of other points were fed into SSNCS, which checked for errors and provided outputs
for the "debugging" of the part program. The students were instructed as to the features and
operations of SSHAC and SSNCS and followed the process outlined in Figure 3. This step in the
course was the longest because of the large amount of interrelated topics which had to be
covered and their complexity. When the center-drilling tape was obtained from SSNCS, the tape
was run on the Slo-Syn and the partially completed part was saved for further machining. After
programming and center-drilling the idler plate, the student was very familiar with the part,
which would be necessary for the operations to follow.

The next step in the programming and machining was the drilling of the holes, which
required tool changes for the different drills used. Because the points had been calculated
previously, the student concentrated on the use and operation of SSNCS and the 1130. Familiarity
and prior experience speeded up the part programming and the machining, despite the added
complexity.

Although the Bridgeport was a point-to-point machine, linear and circular interpolation
part programming was also covered in MT 420, though not actually used. The possibility of
simulating the interpolation by milling an arc with closely- spaced computer-calculated
increments had been suggested previously by the Machine Tool Staff. Experimentation was done to
see if this were actually possible. Using the ARC routine ,of SSHAC with one degree angle
incraments, a tape was produced which machined an arc of reasonable tolerance for student work.
This led to the assignment of the final step: milling the perimeter of the idler plate. At this
critical accuracy, however, SS1AC developed round-off errors which had to be hand-corrected and

257

265

SSNCS FLOWCHART

►

Figure 1

£66

ADVANTAGES AND FEATURES OF SSNCS

1. Card input:

(a) preparation of data in standard 80-column
cards which are easier to read than paper
tape.

(b) Easier program modification — change "unit
record" card rather than sequential paper
tape.

(d) no programmer retraining — cards can be
punched from present Slo-Syn coding forms

2. Listings:

(a) card listing mentioned above (lc)

(b) point listing in incremental steps, incremental
inches, and absolute inches from starting
position.

3. Plotter output:

(a) draws all points, notes tool changes

(b) plots tool path

(d) entire drawing drawn to actual size, within

accuracy of the plotter (on IBM 1627 — + 0.01 in.)

4. Punched tape:

(a) tape punched with the speed and accuracy of the
computer.

(b) tape directional arrows are punched into tape,
along with an operator-readable label and a
label for listing on a Friden Flexowriter.

Table 3

259

267

268

260

PART PROGRAMMING FLOWCHART

Figure 3

‘f *

26 1

269

These points should match.

Milling points

Figure 4

270

262

anotner session of debugging began with SSNCS. The IBM 1627 plotter used has an accuracy of .01
men, but the number of increaants and the accuracy required by the machine tool (.001 inch)
resulted in round-urf errors, and the milling path drawn was almost one-half inch off the mark
(Pigure 4). At first this seemad to be a programming error, but a machining run proved the tape
correct. Experimentation is being done to resolve these problems. The tmal machining of the
idler plate in every case was successful, without computer assist this final assignment would
not have been possiole: program card decks were approximately 550 cards and the tape for the
Slo-Syn was 42.25 feet long, With a continuous path system, this volume would be diminished to
the point whereby manual programming would be a simple exercise.

C one 1 u si on

Students learned and experienced the entire com pu ter- assisted part programming process, it
was entirely "hands-on:" coding, input preparation, running the computer, checking their output,
and finally machining the parts on the Slo-Syn. They also used the computer at various "levels”
of computer-assist, from simple one-shot programs to the complete hardware and software
systems.

Programs were prepared mich faster. Input could be prepared simultaneously by six students
rathar than waiting for one student to tinish with the single Flexowriter. Errors both in
keypunching and programming logic were corrected much more guicxly and eliminated before tney
were run on the macnine tool, wnich may have resulted in damage.

The design of software with simple input requirements, complete diagnostics, and clear
operating instructions, coupled with a computer system that is easy to operate not only allowed
the students to run programs more quickly and with hands-on, but also enapled them to clearly
experience, to a limited extent, what a computet is in terms or nardware and what it can do for
numerical control.

271

263

AN ON-LINE fll N I COflPUT ER IN THE NUCLEAR ENGINEERING CLASSROOA*

Don 5. Hamer and
H. Waverly Graham, III
Georgia Institute of Technology
Atlanta, Georgia 30332

Introduction

An instructional systea has been developed and used in classrooa presentations at Georgia
Tech in nuclear physics, nucleir engineering, and in a joint course with Knory University in
experimental physiology. The coaputer applications to instruction fail into four categories:

1. Siauiation or illustration of physical phenomena by animation

2. Graphical representation of the behavior of mathematical functions
as boundary conditions and parameter changes

3. Computation tisks which accelerate solutions to demonstration
problems

4. Interactive questions and answers (Computer-Aided Instruction).

Experience with these ciissrooa uses has been good. They have been especially effective in
illustrating dynamic processes which are difficult to visualize (categories 1 and 2 above) and
in shortening the time required to explain an instructional point (categories 3 and 4 above).

Tha System Ha rdware

Elements of the systea u
computer is a Digital Equipment
Tektronix, Inc., type 4501
scope display-controller, DEC t
Converter is essentially a »
video plus an RF channel 3 sign
This unit’s outputs and the coi
classroom in the same building,
equipped with a Typrojector[
the instructor and the coaputer
graphical output displayed o
control with enlarged teletype

sed in the classroom are shown in the schematic of Pigure 1. The
Corp. PDP-8/I equipped with an 8R memory ani 65K disk. A
S :an Converter unit which operates in conjunction with the memory
ype 34D (modified), is located at the computer. This Scan
torage oscilloscope with a television raster readout; it provides
al which can drive an auxiliary video monitor or standard TV set.
puter console teletype lines are connected via a patch panel to a
In the classrooa, a large screen TV monitor and a teletype
1] permit student viewing of all control console messages between
as they are projected onto a large screen along with the
n the TV screen. In essence, one has a coaputer under instructor
and memory scope displays.

Applications

With a powerful graphic display capability, classrooa use of the on-line coaputer for
simulation and animation has baen the most extensive application. In each of the examples of
this type to be described, some nuclear phenomenon of microscopic proportions has been given a
dynaiic representation in order to improve student perception of the important features of each
event.

A neutron si
neutrons being
specified by
number generat
of collision
cha racter ist ic
FOCAL[ 2] prog
simulated spec
collisions al
position point
closer the pi
representat ion
example of a t
throughout a o
random neutro
discussion on
significance
emphasized; at
by a listing

owing down and diffusion simulation represents aon oenerget ic
injected, one at a time, into a moderating medium whose mass is
the instructor during the course of the demonstration. A random
or determines the initial direction of the neutron and its point
with a moderator nucleus. The system absorption and scattering
s are determined by statements incorporated in the compact
ram reproduced in Pigure 2. As the neutron moves through

e, its position is recorded at unit time intervals. Scattering
ter its direction and energy and the relative proximity of
s are faithful representations of the particle's speed, i.e., the
otted points, the slower the neutron. Absorption stops the motion
and terminates the track presentation. see Pigure 3 as an
ypical neutron history track. This demonstration is normally used
ne-hour classroom period in which different graphic examples cf
n behavior are employed as the motivation for an instructor
the important parameters of this process, one of central
in reactor physics. At one point the randomness of events may be
another the equations describing the phenomenon may be displayed
of the program itself. As is evident from Pigure 2, the startling

ERIC

265

Figure 1, A Schematic View of the "Mini- computer" - Classroom Graphics
Arrangement for the School of Nuclear Engineering at Georgia Tech.

266

c FOCAL F 11/11/71

01*01 C NEUTRON DIFFUSION IN MODERATING MEDIA; DAVID DIXON# NE705H
0 1*02 TYPE (,THE MASS 0F THE MODERATOR IS '* ; ASK M

01*03 SET P-6;SET PI -3 . 1 4255; IF (FX<2# FX< 1 0 #61 05 ) ) ) i DO 2.45C STORE MOD^
01*05 SET XO*500# SET YO-500; SET PHI»2*PI *FRAN< )J SET V* 555SET RR=1

01.07 SET V-V*RRiIF CV-3) 2.3JSET MUM*-P*FLOG< 1 -FRAN ( > )

01.08 FOR I«0#V#NUM*V; DC 2

01*10 SET CHI-2*PI*FRAN< > j SET PHI-PHI-CHi

01.13 SET RR«FA0SC CFCOS<CHn-<FSQT(FCOS(CHI >?2+Mt2-l )>>/(l+M>)

0 1*15 T

01.20 GOTO 1 .07

02.10 SET XO*XO+FCOS<PHI>*V; SET YO-YO+FSIN (PHI > *V

02.20 SET H 'FDIS <X0# YO )

02.25 IF (1000-YO) 2*4i IF (1000-XO) 2.4;IF (YO) 2.4IIF (XO) 2 .4 J RET
02.30 F I-10#20# 100# I ( FD I S (XO + I # YO ) ♦FDI S< XO- 1 # YO ) ); D 2.35;D 2*36
02*35 I <FDIS(XO#YO+I ) +FD: S (XO# YO- I >+FDIS(XO+I# YO + I > j
0 2*36 I (FDIS(XO-I#YO-*-I)^FDIS<XO«I#YO-I > +FD I S (XO* 1 # YO- I ) )

02. 4C IF <FX(2#FX(10#6102)));GOTO 1.05;C ERASE SCOPE
02.50 GJTO 1 .05

Fit vre -• A Programming Example - Neutvton Diffusion Simulation.

This FOCAL (TM) program is designed to illustrate graphically the step-by-
step history of the process of a neutr<r, diffusing, slowing down, and finally
being absorbed in r ^wo- dimensional homogenous media.

This program was student developed as a "homework" assignment and is a
"Monte- Carlo" solution to the equations for probability of an elastic
collision and the resulting velocity of the colliding particle (lines 1.07,
and lines 1.10, 1.13 above).

The function, FDIS, displays a point at (X,Y) position on the oscilloscope
screen. For purposes of program illustration, the example has the commands
(SET, IF, etc.) spelled out, they could have been abbreviated (S, I, etc.)
to reduce the program storage requirements. As written however, this program
will run in a 4 K-word computer without auxiliary storage.

274

Figure 3, Dynamic Graphical Illustration of the Track of a Neutron Slowing Down
in a Homogenous Media of Atomic Mass 10. The neutron is "borr" at point 1 l ,
fixed speed, its initial direction is chosen randomly. The distance to first
collision (at point 2) is calculated from a second random number, based on the
known interaction probability as a function of distance (exponential attenuation).

On reaching point 2, a scattering direction is chosen randomly, the equation^ for
velocity change for this scattering angle are solved, and a new distance to collision
(at 3) is chosen similarly, etc. (The particle velocity being indicated by the
distance between points.) At each collision the probability of capture is also
determined. In the case above the particle was captured at point 11. If the
particle wanders, in its ’'random wr.lk”,out of the area of interest, a new particle
is generated. In this manner the student can observe the random in- time behavior
of a neutron slowing down in a dynamic fashion.

875

simplicity of the 'rograe encourages on-the-spot modification of the formulas
in order to parsu some student-motivated question or to denonstrate the effect
of a revised absorber or noderator specification.

2. A program which incorporates a ftoote Carlo approach to the understanding of
radiation attanuation utilizes an animation method similar to the neutron
slowing-down application just described. In this demonstration, one
hypothesizes the inpingoaemt of a single gamma ray (or ot!ier radiation) on seme
attenuating material whose composition is specified. Using probabilities which
are determinel by the known interaction propertins of radiation of the
particular ennrgy and material of the specified type, penetration of the
material is calculated and tabulated. I histogram of radiation flux vs.
penetration distance into the attenuator develops on the display screen as each
succeeding ganna ray is followed.* The result is a student "discovery" of the
ezponential nature of attenuation in what is quite literally a computer
experiment. This program is included as Figure 4.

3. The use of different coordinate reference systems is explored in a third
simulation involving elastic collisions of particles in the center-of-mass and
laboratory systems. Properties of these sometimes confusing, always necessary,
alternative reference systems are experienced by changing the masses of target
and bombarding nuclei and observing the effect on final velocities. The adage
that "seeing is believing" is thus well-applied to the lavs of conservation of
energy and momentum.

Closely related in fora to the examples given above is another computer use in the
clissroon which we classify as simulation, the visual representation of a mathematical function
in order to demonstrate how this function behaves as its parameters are changed. Once again, the
simplicity of the FOCAL language makes the function definition and the graphics generation
command structuring task a straightforward one. We have used this techmigue to denonstrate the
solution of coupled dif f eimitii] equations as they describe a radioactive decay problem. This
simulator demonstrates the nature of the decay process by presenting the number of atoms of up
to throe different species which are present as a function of time. The instructor chooses a
single decay chain for illustration of the basic principle, then specifies two or three-
component decay and growth systems as desired to show more advanced concepts, such as
equilibrium. A version of tais simulator has also been applied to the reactor xenon transient
problem.

The third application category which deserves mention is one which might be called
"demonstration solution acceleration." This category covers a large number of computational
programs whose use in the classroom permits a responsive illustration capability and whose use
in the laboratory facilitates arrival at the crucial point of data evaluation without excessive
"crank-and-gr ind" data manipulation of the type students find so discouraging.

In a nuclear engineering course dealing with experimental error analysis, an entire series
of more than a dozen different programs has been developed for illustration and data-fitting to
nunerous statistical distributions which are described in the course text by Philip I.
Bevington. [ 3 ] An undergraduate laboratory in which the radioactive decay of neutron-activated
silver is tine-analyzed using ganna ray detectors and a multi-channel analyzer, the data are
least-squares fit to a tvo-conponent exponential decay curve in order to eeasure the half-lxves
of the two silver radioisotopes involved. A two-hour at-home exercise is transformed into a two-
minute computer operation, permitting each experimental team to compare their results with
published values, disenss differences, and re-run the experiment if necessary, all within a
three-hour lab period. Contrary to what some computer critics might claim, this procedure has
not resulted in any dieinished ability of the students to understand the fitting process.
Evaluation of that capability through examinations has shown that the classroom development of
both the method and the simple computer-stored FOCAL program, coupled with their enthusiastic
experience in collecting data which yield literature-quality values for the half-lives, has
guita adequately and cl most painlessly indoctrinated then in the method. A sieilar experience
has resulted from the use of oar facilities in a pulsed neutron study of the neutron diffusion
paraneters of water, in which a harmonic analysis of the various decay nodes is accompli * by
the PDP-8/I computer. tfithout computer data analysis this rather sophisticated experiment ' ild
not be eearly so attractivn, especially for our undergraduate laboratories. Tet it is one of
the students9 favorites becausn it yields a very real experimental feeling for the time frame
over which neutrons exist in a eoderating medium.

tilong this saee line, our POP-12, with its analog signal input capability, has been used in
a Saoriia Tech physiology course offered jointly with Emory University. Here students were able
to neasure the response of a frog nerve to a voltage stimulus directly through the application
of appropriately located electrodes. On-line signal averaging permitted a continuous data
reduction and refining process, the results of which were displayed in real tine on the
computer's cathode ray tube.

269

876

C FOCAL F 11 n 1/71

01.01 C PARTICLE PENETRATION -MEAN FREE PATH DEMONSTRATION! D.S.HARMEA
01.05 ERASE! IF ( FXC2# FXC 10# 6i 05 > > > I IF CKXC2# KXv 1 0#6102 > ) >

01*10 ASK ?L# T ?

02*10 F X«I#I0#1 020IS Z-FDISCX#50>+FDIS(0#X>IU DRAW COORD

Figure 4. A Graphical Display of Particle Attenuation.

In this program a "Monte-Carlo" solution is made for the distance each particle
travels before collision. On collision, a histogram of number of collisions at
X, within AX vs. X is incremented. As the total number of particles examined
increases, the exponential nature of this attenuation can be observed in the
histogram. The histogram also illustrates clearly the statistical nature of
the interaction process, and the approach to true "exponential" behavior, given
a sufficiently large number of events.

03*10 FOR I ■ 1 # TI DO A

04.10 SET X--L»FL0G<1 -FRAN O* IFOR J*1».5»XJIK CKDl S< J*20# 1 0 > )

04*20 IK < a-49 >4. 3ISET X-50

04.30 StT K-FITit<XI!S HtK)-HiK>*l

04-40 FOR M«K#.2#.7*K!AF <FDISiM*20#50*’HiK>*20 > >

. v,»*< •

, * \ 2.1 0

ERIC

The last sxaapls of coeputatlonal ass stick ss kata ends vitk oar ssall cospatsr is is
criticality calculations, a soat lsportaat ina for asclsar engineers* Classroos ass of tkls
reactivity sodsl of e aaclsar reactor psrslts tks evaluation of a proposed asseubly plas a study
of its sensitivity to changes in geometry, satsrlals# or cksslcal concentrations* It is a
flaxlbls tool for acceleratiag student perception of tke relative iaportaece of tke various
paraaeters la suck a systes*

tke final category of coepater application sltk stick se kave experience is that of
interactive questions and answers* as eost coaeoaly used, tkls refers to a cosputer aided
instruction eevlroneent in stick oely ose student interacts at a ties* Is kave kad success is a
classroos exercise using group cal sltk a tutorial progras in eueber systees* Tke Typrojector
aade tke teletype conversation visible to tke entire class stile tke questions and tutorial text
sere displayed on tke video screen* Enthusiastic participation sas ackleved tkrougk klgkly
interactive discussion aeoag the students about tke answers to sack guestloa posed.

£2H£lE*i2&

tn conclusion, se kava ksd good student response to several types of classroos aed
laboratory applications of an on-line cosputer for slsulatlon of physical pheeoeeea,
visualization of eatkeeaticai functions, coeputatlons which leprove tke learning to effort
ratio, and interactive drill and practice on a group basis* Ruck of tke flexibility of our
particular systee is related to the sleultaneou s poser aed slepllclty of tke FOCkL language sltk
its display coueand structure*

• a portion of tke equipsent used in tkls study sas supplied under a Q* S* atonic energy
Coeeission Grant for equipsent for support of education in luclear Science and Engineering (BIG
Grant Uo* USE 11-69)*

REFERENCES

1* Registered trade eark of Bolt, Beranak, and Nesean*

2* Registered trade sark of Digital Equipsent Corporation*

3* Philip R* Bevington, Md {££&£ Analysis toy Physicists* flcGras-Hlll Book

Coepany, Inc., Res York, lew York (1969)*

»' 278

CORPOTIR APPLICATIONS TO KlRBHATlC STITHBSIS
OP POOR BAR HBCRARISas

Richard C. Schubert
Joseph H- Gill
Raatara flichigan University
talanasoo, flick igaa
Talapkoaa: (61ft) 383-1021

Tha couraa dtCklRill illLl&il ia iaclodad ia tha Ualargraduata Curriculua ia flachaaical
Engineering Technology at Raatara flichigaa University. It involves both kiaeaatic analysis aad
synthesis. Tha analysis is conducted along classical lines whereby velocities aad accelerations
ara solved by analytical and graphical aathods. Tha purposa o f this papar in to discasa tha
kiaaaatic synthesis aspect of tha coarse.

Synthesis, a aabulus aordf ragairas a dafiaition as it relates to tha subject Batter. Ia
dftxkklilft ftMllli! “• restrict synthesis to planar aechaniaaB in general and four-bat aachaaisaa
in specific. For planar four-bar aechaoisas there ara three types of synthesis: 1, Body
Guidiace, 2. Path Guidance, sad 3. function Generation. By way of exaaple connider tha Body
Suidance synthesis problen. Baferring to Pig. 1, suppose tha body shown in to be guided through
tha three discrete positions by a four-bar aechanisn. Those faailiar with kineeatic synthesis
will recall that there is a'n infinite nunber of solutions to this problen. Restricting the
location of the two base pivots, as shown in Pig* 2a, reduces the problen to a unigue solution.
The specific solution is shown in Pig. 2b.

HGUHF

The
coupler,
sunnary,

tha prescribed notion of tha nody. Samples where synthesis is applicable in the aatoaotive
design field include hood hingos, door hinges, rear suspension, and carburator linkages.

BODY IN PLANE MOTION
MOVING THROUGH THREE
DISCRETE POSITIONS

four-bar aechanisn is shown in the first position with the body attached to the
The four-bar aechanisn will carry the body through the three prescribed positions. In
synthesis reguires one to deternine the geoaetry of the aechanisn that will generate

FIGURE 2

The student is presented with two approaches, a graphical a] analytical aet^od. Initially
the problem are designed with the base pivots of the four-bar aechanisn filed. As stated
above, this insures a unigut solution. The student becomes fan* liar with the graphical nethod
and subsequently verifies it with an analytical approach. The analytical approach involves the
sinultaneous solution of thrte equations involving transcendental functions. At this point the
conputer becones the catalyst. An Western flichigaa we have the Digital PDP-10 Tine Sharing
Systan with approiinately IS consoles available to the engineering student. Students are
assigned users' nunbers with appropriate tine allocations. Rather than ask the student to write
the progran to solve the equations, a library prograa in provided. It is only necessary for the
stulent to introduce the data in the proper nannor to obtain the solution. The solution is in

279

tka foci of x aid y coordinates of the noving pivots (ane appendix) • By assigning problnns vitk
unique solutions the stadeat bacoaas faniliar vitk tke operation of tka conputnr - kov to accasn
tha systea, introduce data and obtain ansvnrs, and kov to taraiaata usa of tka coaputac.

All problaas aca not iniquely defined. la tka discassioa abova tka basa pivot locations
vece specified. Consider tha fila advancing aackanisa of a notion pictuca pcojtctoc skovn ia
Pig. 3. Its spacific function ia to aova tha fila dova rapidly (saa path 1) , release, return,
and angagn tke fila agaia (patk 2). This is accoaplishad vitk a fouc-bac aackanisa by axtendisg
the coupler to include the point describing tka path shove. The nnckaniss is driven by a
constant spend notor through link 1. Since tha base pivots (A and B) am located on tke frann
of tha projector and could be attached elsevhera, vho is to say that this is the best design or
evan a good one? Pig* 4 illastrates an altnrnate design that accoapliskes tka sane function,
which is tha batter design?

The concept of design optimization is introduced to the student in UsShanj^sg &1&1XSA3 vhick
dtteapts to ansver this question. Three nain' areas of optinization are considered.

The first considers tha relative size of the four links. If any one link is 10 or nore
tines as long as any other lint then the aechanisa is rejected. The 10:1 ratio is sonevhat
arbitrary, however, fcoa a practical packaging standpoint a liniting ratio nust be observed.
Certtinly a aechanisa vith one link 6 inches long and another link 5 feet long vould be
difficult to package under the hood of a car.

A second criterion considers the transnission angle. This is defined as the snallest angle
betvaen the coupler and the driven link (see Pig. 5). The transmission angle vill vary fron a
uaxinun to a aininun value *3 the driving link is turned. It is desirable to bave the nininua
transaission angle as large as possible. For exasple, if a aechanisa vitk a zero transaission
angle stops in this position, it vould be theoretically inpossible to start again. Purtharnore,
it has teen shovn in the litenture that vide ranging transaission angles result in large
a colorations in high speed operation. It vould be desirable to linit the aininun transaission
to 40 degrees, although this is not alvays possible.

FILM FEED
MECHANISM

FIGURE 3

FIGURE 4

FIGURE 5

100-

90 So 2^0 3&T’ 6

DR VINS LINK ANGlF

DRIVEN

LINK

(TRANSMISSION

ANGLE

BASE

274

Thm third criterion considers the classification of sechanisss. Sose four-bar sechanisss
will have no link that can turn through 360 degrees, thus eliminating then fron an application
with constant speed notor drive. On the other hand soae nechanisas need not turn J60 degrees,
such as hood hinge mechanisms. Hardings Inequality Method can be applied to a four-bar mechanise
to determine if it is the class of nechinisn that will or will not rotate through 360 degrees.

Although this comprises only soae of the criteria for which a design nay be Judged it
gives the student a basis on which to choose. All of the af orenentioned nethods have been
progrnnned and included in tha computer library. Bather than one computer program to cover aii
tha criteria, each has been pragranned separately, thus giving the student the option of using
than individually or as subroutine of a general program that he develops.

A tern project is assigned to the students in which the notion of a body is to be carried
through three positions as shown in Fig. 6. However, in this case, tha location of the two base
pivota are restricted to area locations. It is observed that for each location of base pivot b
there is theorot icnlly an infinite number of possibilities for pivot A. The converse is true
whan pivot A is fixed. This constitutes a double-infinite number of solutions - a typical real
world design problen. Students are given approximately 8 weeks to explore possible combinations
to arrive at the best solution based on optimization criteria. Results are compared the final
week of class.

In sunnary, the student fmiliarized himself with the computer programs after first solving
problems by conventional nethods, i.e. , graphical or nathenatical solutions using annual
techniques such as slide rile or desk calculators. He then applies these concepts to a term
project whore the design is virtually open-ended and results must be justified based on
optimization criteria. in this way, the student studies the initial results of computer output,
analyzes the data, and then resubmits information to refine the design. He thereby controls
the destiny of the final design.

APPENDIX

A computer program for body guidance synthesis is written in basic language. It
incorporates the input routine rather than the read-data method. This gives the student more
flexibility since he can immediately introduce new data~contingent on the output of the previous
calcu lation.

Consider a body that is to nove through the three positions in Figure A1. The two fixed
pivots are located as shown. By setting up a convenient coordinate systen with the origin
located at one of the pivots, the corresponding x and y coordinate of a particular point on the
body is determined (XI, Y1, X2, T2, X3, T3). The angle of rotation of the body is then
determined with counter-clockwise as positive (T2, T3|. Computer input-output is as follows:

Enter

*0.

7 0,0
Enter

11.

12 ,

* 1.

2. 3

Enter

Y2,

7 1,

0. 2

Enter

r 2,

? 30.

X - coordinate * -2.2791 [Conputer output for moving pivot attached to

I - coordinate * 0.29975 fixed pivot A. ]

Enter IQ, TO
7 3,0

Enter XI, X2, X3

✓

1 1. 2, 3
enter II, 12, 13
M, 0, 2
enter T2, T3
730, 60

Z - coordinate ■ 1.1 ?97 [Conpatar output Cor noviug pivot attacked

I - coordinate ■ -2.6961S to pivot B. ]

r ha

nechanisn is shown

in the first position in Figure 62 with the body affixed to the coupler.

FIGURE A

0ty

AN ANALOG JDMPCToH OPTIMIZED FOR UNDERGRADUATE INSTRUCTION

Stephen G. Margolis and Hinricn R. Martens
Stite University of New York it Buffalo
Buffalo, New York 142 1 4
Telephone: (71b) BJ1-5J21

lQ.L£2diiC t ion

In tne teaching of coirsos winch introduce the undergraduate student to dynamic, t me
dependent aspects in tne m it nomatical and physical sciences (i.e., electrical circuits,
dynamics, differential equations, etc.), we nave always sensed i need to illustrate the
associated mathematical equations in i simple and qualitative manner. Considering various
possibilities, incluling movies, viieotapos and time-shared lijital computer terminals, wo hive
concluded that a simple analoj computer capable of repetitive operation would be ideally suited
to meet this need. however, commercially avail a ole analog computers require some degree ot
proficiency in programming and assume that the ^udont (anl his instructor) nave a certain
amount or inclination towaris electronic hardware. These factors hive always created a oirner
pravanting a fuller utilization ot analog computers in introductory mathematics, physics and
engineering courses.

In this paper we describe the SUNYAC, a special purpose analog computer which is intended
solely tor use in the instruction of undergraduate students at the sophomore through senior
level. This computer differs from other available analog computers in that it was designed from
the ground up to oe a tool ot instruction, not a tool ot research. Consequently, Lts principal
object is not the precise solution of differential equations; rather, its obgect is to be a tool
by which students will gain insight into the structure and meaning ot differential equations and
into tne properties of their solutions.

How does this machine lifter from commerically available analog computers? Primarily, it
differs by accepting a more restricted set ot problems and in exchange oftering much greater
simplicity ot programming anl operation. For example, the student wires up nis problem using a
maximum of eight wired connections. In many cases fewer connections are required; for instance,
for a differential equation of the type dy/It ♦ a y = constant, three connections are necessary:
ona for the left hand side of the equation; one for tno right hand si do and a last one tor the
display oscilloscope. The coefficients are set by a tew slide switches and then the solution to
a problem is immediately available in real time as a meter deflection, or as an oscilloscope
display refreshed forty times per second. Typical setup time tor any problem is lens than one
minute. In contrast, commercially available analog computers have more complex wiring, require
that coefficient, potentiometers be set *>y indirect means, and do not always provide oscilloscope
display of repetitive solutions. The cost of the SUNYAC is less than *1,000, including the
companion oscilloscope, a price which encourages the availability or enough of these machines
tor hands-on use oy every student.

It is readily granted that this little analog computer trales-otf flexibility tor
simplicity. But in the intendel application these losses are more than offset oy its low cost
and extreme else of patching and coefficient setting. As a consequence, practically no
background or prior preparatioi in analog computer tneory is demanded of student or instructor.

Design of. tne 1 a c n_in e

The salient design features of the SUNYAC are as follows:

1. integration and summation are performed by operational amplifiers using tield-ettect
transistor (FGT) input stages.

2. Mode switching m both the manual and repetitwe modes or operation is performed by
complementary symmetry metal-oxide-silicon (C OGnJS) solid-state switches. Thus no
mecnanical relays or choppers are needed.

3. initial conditions are hard wired to tne integrators. Initial conditions are
restricted to 21 integer values between -10 and *10 volts (including zero); tnese are
set in ny four switches using binary-coded-decimal coding in a 122b sequence. Each
integrator may have up to four inputs.

4. six coefficients are available each of which is step adjustable to 41 values between
0.05 and 2.05 in increments of 0.05. Each coefficient is controlled by six switches
and is set using binary ~oded decimal coding in a 1225 sequence.

211

✓

Forcing
Funct ion
Genet ate r

■O

Time Base

Inverters

Coefficients Integrators

FIGURE 1 . Layout of the Computer

278

Figure 1 i s d schematic layout showing the coaponants available in the computer. The
computer consists of a forcing function 4enerato»:, a time base, six adjustable coefficients,
three integrators with integral initial condition switches, and two inverters. Normally, each
integrator has two coefficients associated with it, but, it necessary, two other coefficient
may be borrowed trom another integrator. The physical layout of the computer is shown in Pigure
2. Trie coeificient switches are arrayed on the left side of the m am panel. The five switches
wtiicci control the magnitude and size of the initial conditions for each integrator are arrayed
down the center of the main panel. Below the^e switches are the outputs or each integrator. The
iu;uts and outputs tor the three inverters are located in the near right hand corner of the
lower panel. The controls for the function generator are located along the right side of the
lower panel. (Not visible in figure.) In non~repet 1 t 1 ve operation, the selector switch located
under the meter allows the meter to real the outputs of the three integrators, the two summers,
and the function generator. In repetitive operation, the same switch selects the signal t*»»t tr
t hi Y-axis of the oscilloscope. The mode switch, located in the right center of the main panel
selects the mode of operation of the computer. In the "initial conditions" made, init-.?l
conditions are set. In "hold" mode, all functions including the time ease are frozen, and i.n
"operate" the differentia1 egiatiOii* are solved. By turning the switch fully counter clockwise,
the computer is put into o "repetitive operations" mode in which the time scale is speeded up
by a factor of 1,000 *nd the oscilloscope picture of the solition is refreshed forty times per
second.

Figure J shows all of the connections ar.d settings which are necessary to solve the set of
differential eguations:

Figure 4 shows the connections and
differential eguations:

xx(o) - 9,
x2(o) - 5.
x^(o) * 10.

switch settings required to solve the simultaneous

. o
ERIC

v * -0.5v - 1.5x v(o) * 9.

x « -v x(o) « 5.

Circuit Details

In order to realize the educational objectives of the S UN I AC some novel design features
were devised. Of the design r eg u i remen ts, the most prominent was the requirement for rapid
refreshing of the oscilloscope display which led to the use of a solid-state integrated-circuit
switch in mode switching. In tarn, the use of these solid-state switches simplified the overall
design and reduced the cost.

The basic unit in tha operation of the computer is the integrator. Four identical
integrators ace used in the computer, three in the solution of equations, and the fourth to
generate the time base. The integrator circuit diagram is shown in Figure S.

Referring to Figure tha upper COSMOS switch is closed in the initial condition position,
connecting the initial conuitions network to the operational amplifier. The two back-to-back
silicon diodes provide over-voltage protection for the COSMOS. In the hold position both COSMOS
switches are open. In the operate position the "ic" COSMOS is open and the "operate" COSMOS is
closad connecting the coefficient network to the summing junction. Ag; in, back-to-back diodes
provide protection tor the COSMOS switch. The coefficient switches connect the input resistors
in parallel. For example, to obtain a coefficient of 0.75, the .5 switch, one of the .2
switches, and the ,05 switch would be closed. Note that one end of all of the input resistors is
connected to the input teninal and that, depending on the switch position, the other end of
eacn resistor is either connected to the summing junction (a virtual ground) or to ground
itselt. Thus, as seen trom the input, the input resistors all appear .to be connected in parallel
and represent a constant impedance which turns out to be 0.488 megohms. Because tha input
impedance is thus fixed, tne design of an attenuator to extend the range of tue coefficient, if
desired, would oe very simple.

During repetitive operations, the "ic" and operate COSMOS switches are alternately closed
and opened. The wave-forms required to perform this function are generated by an asymmetrical

t ;

iSS

FIGURE 4, Patching for a System of Two Simultaneous Equations

ERIC

IC Sign

+ 0

FIGURE 5, Intergrator Circuit

From Time Base Upper Lower

Limit Controls

FIGURE 6. Schematic of Function Generator

multivibrator,. The circuit jsed t j generate the tile base is identical to that used for the
other integrators except that its initial condition is fixed as zero and a single input resistor
is used to generate a sloae of one-half volt per second. Thus, the tine base voltage is a
triangle wave which starts at zero and reaches ten volts in 20 seconds, in the slow mode.

In the slow node of operation, the tiie base lay be used to operate an x-y plotter or the
horizontal axis of a storage type oscilloscope. In the rep-op aode of operation, the tiie base
is speeded up by a factor of 1300 so that it goes from zero to ten volts in 20 ii lliseconds.

A bloc* diagram of thJ function generator is shown iu Figure 6 and sole typical output
waveforms of the function generator are shown in Figure 7. As can be seen in the figure, the
function generator can generate pulses, step functions, and one-step staircase functions. With
the use of one integrator ramp functions can also be generated. In switching froi slow to
repetitive operation, the tin* scale of thest .unctions is a u tola tical 1 y speeded up by a factor
of 1300, while the amplitude scale is left unchanged, other functions, such as exponentials and
sinusoids can be generated by appropriate connections of the integrators of the lain part of the
compu ter.

A EEli ca t i on s

Tne SUNYAC was conceived in the spring of 1 97 1 with a prototype constructed by early
summer or 1971. Since then it tias been actively tested and a second improved model has been
constructed. It has been exposed to a nuaber of different applications which are briefly
summarized here. These will testify to the versatility and convenience of the SUNYAC.

a. The prototype modeL of the coaputer was used during the suaner of 1971 in a workshop
on differential equations (sponsored by the National Science Foundation) attended by 27
faculty members from 9 community colleges in New fork State. This workshop dealt with a de-
tailed analysis of current practices and new trends in the teaching of elementary
differential equations. The SUNYAC was included in this analysis. One of the
recommendations emerging from the workshop report consists of encouraying teachers of
differential equations to demonstrate the qualitative nature of solutions to differential
equations usiny an analog computer. A partial listing of problems for student solution
whicn were proposed and i op lemented using the SUNYAC follows:

Simple exponential solutions
Damped sinusoidal solutions
Superposition of solutions
Compound interest problems
Fluid mixing problems
Simple vibration

RC, RL, and RLC network problems

Demonstration of the impulse as the limit of rectangular and
exponential pulses
Radio-isotope decay chains

b. During tn^ tall semester 1971 the computer was used by faculty members of SUNY at
buffalo to den^nstrate to a -junior class sta te- variable solutions using the concept of the
matrix exponential . It was also used to demonstrate to a sophomore class in Electrical
Engineering the effect of varying the initial conditions of a second-order differential
eguation, to demonstrate the effects of varying the damping ratio and to illustrate
graphically the concepts af underdamped, overdamped, and critically damped solutions.

c. At the present time the second version of the coaputer is undergoing evaluation at
Corning Community College for use in a course in differential equations intended for math
majors, science majors and pre-engineering students.

These and othej. similar applications lead us to conclude that SUNYAC offers.no programminy
barriers to students and instructors who are untrained in the use of analog computers. By virtue
of its simple and direct features even a person totally new to analog computing can master it?
operation within one hour.

A manual complete with operation instructions and fully worked out sample problems has been
prepared, reflecting experience to date.

Concl usions

Two models of SUNYAC, a special purpose analog computer optimized for use in instruction,
have been designed, built and tested. From the student*s point of view, the performance of
SUNYAC is equal to that of more expensive and elaborate commercial analog computers, but SUNYAC

Step Functions & Pulses

Ramp Functions Generated with
Function Generator and One Integrat

FIGURE 7. Function Generator Waveforms

is Much sinpler to prograa and operate. The setting ot coefficients and initial conditions is
direct and simple. No hardwire considerations intervene between a student#s thinking about
changing a coefficient and his actual iapleaentation of the changed coefficient on the Machine.
The results of changes in coefficients and initial conditions are ^aaediately apparent to the
student on the oscilloscope scr *en.

Based on use so far, it appears that Machines of the SUNYAC type are well suited for
second-year courses in differential equations, circuit analysis, and dynanics. in such
applications, the aachine should prove particularly attractive to two-year colleges in view of
their relatively United budgets and their linited need for research- or ien ted Machines. Because
of the low cost of che Machines, it should be feasible to provide enough Machines to give every
student hands-on experience with the nachine solution of ordinary differential equations.

For four year colleges, ^ur experience to date with the nachine indicates that it has value
in teaching sophonore and junl.r engineering students about the fomulation and solution of
state equations. With its capability of dealing with third oLier systens, it can sinulite lost
of the salient properties of linear control systems as taught to seniors in first courses in
lineir control. Thus we sea this as a nacniae which has applications in courses at the
sophonore, junior and senior levels in the undergraduate curriculun in engineering, natheaatics,
and science.

ACKNOWLEDGEMENT

Two nod el s of the SUNYA- were constructed by Mohammed Motiwala, with the assistance of our
technicians A. Longley, W. Willerth and W. Berent. Photographs in this report are by williaa
flargolis. This research was supported in part by NSF grant GY 6593.

SPATIAL HODEL BUILDING IN THE SOCIAL SCIENCES

Philip H. Lankford
University of California

Los Angeles, California 90024
Telephone: (2U) 825-1071

Although the use of computers has now become an accepted tool of social sciences research
in qeography, the iepact upon undergraduate education has been slight. If the student is exposed
to computers, it is usually not jntil a quantitative aethods course late in college. This paper
reports the great success of using the conputer in a freshaan class as a tool in spatial aodel
building •

Geography 1c, Introduction to Locational Analysis, is the final course of the three quarter
sequence required of all qeography .. ijors. The course is open to freshmen, but since very few
students enter college as geography aajors, aany of the students are juniors or seniors.
Lectures introduce the students to central place theory, agricultural location theory,
industrial location theory, interaction aodels, and urban-regional growth aodels. The laboratory
part of the class consists solely of conputer exercises in spatial aodel building.

The General Problea

The general assignaent for the quarter is to develop and test a spatial aodel. The student
is to choose a current problea of social concern, such as poverty, as a topic of research. Using
the theories and aodels developed in the lectures, the student deduces stateaents about the
spatial coaponents of the problea. After checking census aaterials, testable hypotheses are
developed about a specific variable and its relationship to several other variables. The chosen
variables are coded onto eighty coluan sheets, observations are recorded for a contiguous group
of counties or tracts, or for cities within a region, depending upon the particular problea.
After the data are keypunched and corrected, the specific hypotheses are tested with a siaple,
two-variable regression program, QXKBEG. The student then aodifies his siaple descriptive aodel
based on the results. A second assignaent produces, with the STRAP program, contour naps of the
oriqinal variable being "explained” and residuals froa the significant regressions. The student
then prepares a final report, drawing conclusions about his spatial aodel and commenting on the
difficulties encountered.

The first point of the laborat:>ry discussions is that the scientific method can be applied
to geographic probleas in the social sciences. Hypotheses can be drawn from existing theory,
tested with existing data, and conclusions drawn about both the real world and theory.
Specifically the student is to deduce a descriptive model regarding the spatial variation of a
current social problea.

Current problems in U. S. society are chosen for several reasons. Ey contrast to other
topics, student interest is sparked with discussion of such problems. Everyone has an opinion on
the problems ana solutions. During discussions the students also realize the policy and
political iaplications of the aany theories and models given in the lectures. The particular
problea studied is up to each student. As an example, after a discussion of poverty in the
United States, one student nay wish to examine the distribution of family median income or
percent families with incomes under S3. 000 a year, for counties in California, or median incomes
for the forty largest cities of a state.

After identifying the research problea, specific testable hypotheses are constructed.
Considering theory and data sources, the student develops several simple, two-variable aodels in
the fora Y * f (X). Froa the lectures and outside readings the stude t is also able to state the
direction of the relationship, its spatial variation, and the explanatory power of the aodel.
One of the instructional aims is readily achieved. Host students have a preconception of the
census as an all eabracing source of information. Disillusionment quickly develops as they
realize that few of the socio-economic variables actually measure the probleas under
investigation.

The Class

Methodology

285

Association Versus Carnation

The iaportant difference between association and causation is emphasized, since fee
students have consciously understood it. Two examples are useful. Is a region with a nountain
chain, rainfall is greater at higher elevations due to cooling as clouds pass over the peaks.
The association between elevation and rainfall also inplies a causal chain. Increasing elevation
will increase the rainfall, but increasing the rainfall of an area with artificial aethodsv such
as a cloud seeding, will not iacrease the elevation of an area! in contrast, the association for
villages between nusber of storks and nunber of births does not imply causation. Larger villages
have a larqer nusber of births, and a larger nusber of chimneys, favorite nesting places of
storks, and hence larger stork populations, however, the causation is not direct; increasing
stork population does not bring about sore babies! Instead the "causal" chain operates through a
third variable, total population. Symbolically , the sinple causal chain between rainfall and
elevation is Rainfall = f (Elevation), or if a straight line is used for causation:

The curved line shows association (correlation) between the two variables. The use of 'inch
diagrams greatly clarifies the construction of nodels and their interpretation.

Preparing the £ata Deck

After designing the specific nodel and corresponding selection of variables by appropriate
observations fron the census, several mechanical steps exist. The data nust be placed in eighty
column coding sheets. Since less than one percent of the students have any faniliarity with
keypunching, copying data in tabular form precisely in appropriate columns is a very iaportant
step. The regression progran, QIKREG, uses a fixed input foraat. The students use five variables
in fields of ten columns each (5F10.0), and the last thirty colunns for identifiers. They are
instructed to place each data entry in the appropriate field, right or left justified (the
student's choice) , with a decimal point and no embedded blanks. Experiments with teaching format
specifications and variable format was a disaster. A little knowledge of such things is
dangerous since the students are more creative than FORTRAN is flexible. Format free input using
NAMELIST procedures and new options available in Release 20 level H FORTRAN also proved to be
too difficult, since explanations proved too elaborate to be absorbed by the novice.

Keypunching proved easier to teach than initially expected. Shif * , automatic feed, and use
of the duplication key to correct errors proved to be easily learned.

To aid in correcting any keypunching errors, a special computer procedure was used to list
the card deck. Essentially the program simply copies the card., onto paper with the standard line
printer. Such a procedure allowed greater ease in checking the deck. However, since the list
procedure rarely fails, its use has an additional benefit in removing fear of the black box.

Fear and the Computer

Even in this day, despite the common use of punched cards for paying bills, and
computerized registration procedures at UCLA, utudents still view the computer as a mystical,
all-knowing being. Lectures about how a computer works does little to allay fears. Binary
mathematics and switching circuits only add to the mystic. It is important to simply emphasize
that the computer is only a dumb beast; it can only do, and does, exactly what it is told. For
one thing, such an approach to the computer makes the student realize that whea a job fails, it
is his mistake and not an error in the progran or the computer. The responsibility rests solely
on the student to prepare his input deck carefully, correct all errors, and recheck his deck*
Secondly, the approach helps to alleviate fears of the computer "knowing" everything or being
capable of "thought."

Statistical Aa&UaiS

Once the basic data deck is ready for analysis, an introduction to statistics begins.
Returning to the discussion of specific hypotheses, T * f (X) , is restated in the linear fora, X
- a+bX. The complete regression curve family is acknowledged, (curvilinear, polynomial, etc.).

Rainfall 4

Ele vation

The association, Births * f (Storks) actually is the causal chain

but the ninple, linear regression sodel with one independent variable is sufficient as an
introduction.

Bather than turn to correlation , which experience showed to distract fron the discussion,
we continue on the sinple linear nodel. Scatter graphs with the estinated regression line drawn
denonstrates the leaning of sun of the sguared deviations. Later, the sane type of graphs give
leaning to residuals fron the derived equation. Many students are content for purposes of the
laboratory discussion, that 'a' and • b* are unique, but it helps to convince the, ^oubters by
actually shoving with a little calculus how the coefficients are derived.

0~ce an equation is derived the statistical significance and percent variation explainea
are very inportant in nodel building. The significance of 'b* is explained in nonnathe.’iatical
terns of confidence of 'b' as a predictor, or replicator, of the original data. A widely
dispersed ncattergran gives a poorer predictor 'b1 than a narrow dispersal of points about the
actual regression line. The QIKREG progran conputes the corfidence Units for 'b' and prints a
nessage for the student when the 95% level is attained or exctnded. The progran also conputes R-
sguared and prints the percent total variation explained. The relationship could be significant
at the 0.05 level but still explains only 25% of the total variation. The significance and
"power” of each relationship is the k^y to the construction of the student's spatial model.
Residuals are conputed for each regression as the deviations often nave spatial patterns
inportant to the interpretation and developnent of the nodel. QIKREG sanple output is shown in
the paper. Thf; students prepare a brief, five-page paper reviewing the hypotheses, data sources,
each regression nodel and results, and their nodel of spatial variation.

The second assignnent is a brief report on the spatial pattern of the nodel. Using STRAP
the student produces contour naps of the chosen dependent variable and residuals fron each of
the significant relationships. STRAP requires several input aubdecks: (1) an A-OOTLINE package
consisting of the keypunched arbitrary grid coordinates describing the outline of the study area
to be napped, (2) -DATA POINTS contains the coordinates of the observations, such as centroids
of counties or location of cities, (3) REVALUES contain the values of the variable to be napped,
and (4) P-flAP has the paraneters of the nap such as si2e, nunber of contour intervals, >lze of
each interval, etc. The progran is very flexible, but for sinplicity, the students are told
about only a snail aunber of options. The visual display of variation is extrenely useful to the
student in drawing conclusions about his spatial nodel.

The conputer Proqpans

All student jobs are run on UCLA's Canpus Computing Network's IBR 360 nodel 91 with 4#000K
storage available to the user. A listing of QIKBBG, written by the author, is given at the back
of this paper. STBAP was written by Harvard's Laboratory for Conputer Graphics. Load nodules for
QIKREG and STBAP are kept on resident disk packs and are invoked by sinplified procedures which
eliminate JCL problem for the student. The QIKREG progran, written for 100 observations, needs
only 128K of storage and the average student cost for four regression nodels is 10.40 for 1
second and 100 XO requests. STRAP by conp&rison is very expensive. Using 2S0K (with no overlays)
the average student job uses about 120 seconds and 2,000 10 reguests, or about 110.00 for four
naps. Hith an average of thirty students each quarter, the average overall cost is roughly $100
for the quarter-course.

Success

Based on exanination perfornance, interviews, and questionnaires, of over 120 studeuts
during the past year and one-half, the success of the spatial nodel building iaboratory with a
conputer has been very great. The pace of the laboratory discussions with aid fron the teaching
assistant keeps even the nost nonscien tif ic student interested. At the sane tine the ability to
experiient and explore the regression technique and the nunerous options of STHAP keep the
advanced and relatively conputer-sophisticated student excited. The students realize fron their
research that scientific nethodology can be applied to social geography and that theory can be
tested, refined, and developed further. The difference between association and causation becones
fully appreciated and the students gain a lore critical approach to theory in the social
sciences.. An introduction to statistical techniques and napping with a conputer allows higher
level courses to cover wore advanced topics since fundanentals are wore easily absorbed.
Learning the linitations of the census is an aid to sone students in later research. Keypunching
is a skill many students find useful, and for a few even profitable during their college years.
At least one student even chauged career plans, and now is enployed as a conputer progranner for
a planning firm producing computer naps.

ALTHOUGH THIS PROGRAM HAS BEFN TFSTEO BY ITS CONTR IBUTER

t NO

QKRG0100

MARR ANTYV FXPRE SSEO OR IMPLIED, IS MAOE BY THF CONTR IBUTER OR THE
UNIVERSITY OF CALIFORNIA, AS TO THE ACCURACY ANO FUNCTIONING OF

0KRG0120

0KRG01*0

— e —

PROGRAM AND RELATED PROGRAM MATERIAL, NOR SHALL THE FACT OF THE
DISTRIBUTION CONSTITUTE ANY SUCH WARRANTY, ANO NO RESPONSIBILITY

“Ts ‘ "a ssumed'by'the " c ont r irut'eT'or ' the' UNI VERS 1 f Y -OF ca'l i form I a, in

CONNFCT I ON THEREWITH.

0KRG0160

QKRG01B0

qkrg6?o6

QKRG0220

OIKREG

LANKFORD, DEPT OF GEOG. UCLA

QKRG0240

QKRG0260

OCTOBER 1971

DI MENS ION T( 20) ,FMT( 20 ) tX( 1 00) tY( 100) ,YC 1 1 00) tRESI D( 1001 1

0KRG02B0
DTI 100,7 ) 0KRG0300

r I MENS ION XYV (100,5)
REALM XNAME , YNAME

0KRG0320

QKRG0340

1000

OAT A BLK / * «/, OO/*????????* /

READ 15*1 9* END3 2000 ) T

QKRG0360

0KRG0380

FORMAT I20A*)

READ (5»32»FND* 3000) N,MXO

QKRGOAOO

QKRG0*?0

FORMAT (!l f 2X ,13)

okrgo**o

QKRG0*60

iOi

WRITE (6,161 ) T,N,MXO

FORMAT 1*1* ,20A*//*0NUMBER OF VARIABLES «* I3/'0NUNBER OF

0KRG0480
OBS ERV AT I OK R GO 500

•ONS *• 131
C ERROR SECTION

QKRG0520

QKRG05A0

IF (N.Gt.5) GO TO 201

IF (N.LT.l) GO TO 202

QKRG0560

0KRG0580

IF (MXO.GT.)OO) GO TO 203

IF (MXO.LT.l) GO TO 20*

0KRG0600

0KRG0620

GO TO 400

0KRG06*0

QKRG0660

o
o c

WRITE (6,2010) N

FORMAT CONUMBER OF VARIABLES GREATER THAN ALLOWED* ,16)

QKRG0680

QKRG0700

202

STOP

WRITE ( 6# 2020 ) N

0KRG0720

0KRG0740

2020

FORMAT ( • ONIJMBER OF VARIABLES LESS THAN ONE*, 16)

STOP . .

QKRG0760

..asBisozaa^.

203

2030

WRITE (6,2030) MXO

FORMAT ( • ONUMBER OF OBSERVATIONS GREATER THAN ALL0WED*,I6)

0KRG0800

0KRG0820

204

STOP

WRITE (6.20*0) MXO

QKRG03*0

QKRG0860

2040

FORMAT CONUMBER OE OBSERVATIONS LESS THAN ONE*, 16)
STOP

0KRG0880

OKRGO905

400

DO 60 1=1, MXO

READ (5,205) ( XYV( 1 , J) , J=l ,5 ) j ( DT ( IjK ) _,K=1 , 7)

OK R GO 970
0KRG09*C

205

FORMAT (5F1 0.0,7A*I
DO 1500 KK=1 , 7

QKRG0960

0KRG0980

sx=o.

SY=0.

QKRG1000

QKRGI020

SXY=~0.
SX2-0 •

0KRG10*0

QKRG1060

SY230.

SDFVX=0.

OKRGl 090
QKRG1100

SDEVY=0.

QKRG1 1 20

..a_K.R_Qll*0.__.

C OPERATIONS BEGIN HERE

C PROBLEM CARD _ „ _ .

0KRG1160

.0KRGU80.

READ (5,?0,END=2000 i I OEP , INOFP ,YNA PE, XNAME

QKRG1200

FORMAT (2II.2A8)

0KRG1220 .

f* IX'NA'MF.t 6.61k) xname=6o
IF ( YNAME. FO.BLK) YNAME=00

OKRGl 2*0"
OKRGl 260

IF ( IDEP.LT • 1 ) GO TO 501
IF ( IDEP.GT.N) GO TO 501

0KRG1280

9KRG1300

IF ( INDEP.LT. 1) GO TO 50?
IF IINDEP.GT.N) GO TO 50?

OKRGl 320
QKRGt 3*0

501

GO fn 550

WRITE (6,5010) IDEP

OKRGl 360
OKRGl 380

5010

FORMAT! *ODFPENOFNT VARIABLE INOEX INVALIO FOR THIS ANALYSIS »•
♦•OGOING TO NEXT CARD*)

16/

0KRG1*00

0KRGl*20

GO TO 1500

QKRGI**0

288

224

502

WRITE (6,5020) (NOEP

QKRG1460

5020

FORMAT! ’ 6 INDEP FNDEN t VARIABLE 1 NOE X INVALID FOR THIS ANALYSIS »
*i6/'0r,niNr, to nfxt Faro*)

• tOKRGIAaO
OKRGl 500

550

r,0 TO 1600

on 73 j=i , mxo

OKRGl 520
OKRGl 540

XI J)=XYVI J, INOFP)

Y ( J)=XYVI J, IDF®)

WRITF I 6 t TO ) IDFP, YNAME, INOEP.XNAMF

FORMAT I • O’ , 'OFPFNOFNT VARIABLE NO. • , 1 9 , 2X , A8/ l X , • INOFPENOENT

OKRGl 560
QKRGL580
OKRGl 600
VOKRGl 620

♦ ARI8LF NO.*, I 8 » 2 X , A 3 )

OKRGl 660
OKRGl 660

00 58 K = l , MXO

OKRGl 680
OKRGl 700

SX«SXfX<K i
SYsSYfY( K )

OKRGl 720
OKRGl 740

SXY=SXYH X(K)*Y(K) )
SX2=SX2*( X I K 1 •* 2 I

OKRGl 760
OKRGl 780

SY?=SY?f( Y(K ) **?)

OKRGl 800
OKRGl 820

XPAR=SX/MXO
Y« AR= S Y/M XO

QKPG1840

J2KPGL&40

SMX?=6X7-X8AR*SX
^MY?=SY2- Y^AR*5Y
SMXY=SXY-XnAR*SY
VAR Y=SMY2 /mxo

OKRGl 880

0KRG1920
OKRGl 940

VARX=SMX?/MXO
SOFVY=SORT (VARY)

OKRGl 960
QXRG198G

SOF VX=SOR T( VARX 1

R=SMXY/SMX? .. ..

A=Y8AQ-(H*X8AR)

F V=**SMXY

0KRG2000

._.0X«J12Q.?a__

0KRG2040

0KRG2O6O

R? = F V/ SM Y 2

R=S0RT(R7 )

0KRG2080

QKRG21Q0

R=SIOM(R, 9)

S S 0 E V = 0 .

00 59 L=l , M VO
YC(I )=A«-T*X(L )

0KRG2120

...0KBG21A0...

0KRG2160

0KRG2J.80

RF S lf)( L ) = Y 1 L j— YC 1 L 1

SSOF V= SSOE V* I I Y(L )-YC(t» )**?)

0KRG2200

0KRG2220

SFRR=SQRT( SSOEV/MXO)

0KRG2240

QKRG2260

SF° R= S FRR / ( SO FV X* SOR T ( FLOAT (MXO) ) )

0KRG2280

0KRG2300

WRITE (6,11 YBAR,XBAR ,SOEVv ,SOEVX,A,B, R2,R QKRG2320

FORMAT CO' i 51 1 1 H— I.'STATI STGKRG2340

«■ I r A l ANALYSIS’, 54()H-)///10X,’MFAN Y = • , F 20 . 5/ 1 OX , ’ MEAN X =’,F?0

. 5QKRG23 60

* 7/lox, »s'TANb"APrj deviation of y =•, f?o. 5/ibx, • standard bEviAflON

*F X =• , F 20. 5// 1 OX , • Y INTERCEPT = • , FI 4. 5/ 1 OX , • B =’,F?4.5//

OOKRG238!)

QKRG2400

* //10X, ’COEFFICIENT Of-' OF T F RM I N A T I ON = * F 1 5 . V 10 X, • CORR El AT ION CDEFQKRG2420

♦ FtriFNT = * , F 20. 5/ / 1 0KRG2440

IF (ABSI R).GF.1.98*ABS(SFRB)J WRITE (6,51

FORMAT COP EXTFFDS" TWICF ITS STANDARD E RROR ' / IX, ’ R EL AT I ONS H IP Cl
*F I OFNT AT 95 f LEVEL’PX , ’CONGRATULATIONS’ 1

QKRG2460

0KRG2480

0NQKRG2500

0KRG252O

C R FS IOUAI s ’l

QKRG2540

0KRG256O

WP 1 TF (6,141

FORMAT! ’O’, 40X, ’RESIDUALS FROM R EGR E SS I ON • / /32 X , • OB SER VFO VALUE’

QKRG2580

.6QKRG2600

♦ X, ’roMPUTFO VALUE' , llx", • RES I OU AL •/ IX , • C ASF • , 15 X~, • X • , 18X, •¥• ,I5X
*Y I C ) ’, 19X, ’Y-Y(C) •//*

, ’0KRG2620
0KRG2640

no 96 1=1 , MXO

WRITF (6,2 7) L,XIL) ,YCL),YC(L) , RES I 0 ( L 1 , (DT(L,K) ,K = 1j7)

0KRG2660

0KRG2680

9ft

FORMAT ( IX , I 4, 4FX0.3 , 5X , • I ’7A4,’ )•)
CONTINUF

0KRG270U

0KRG2720

1500

CONTINUE
GO TO 2000

QKRG2740

0KRG276O

3000 WRlTE(6,30tO) QKRG2780

3010 PHRMA T ( • 0 SOMF TH I NG FOULED UP. END OF OECK WHJ I L E _ TR Y_I NG_ _Tfl ^_R JE L A0_C0PKRC2_80q

♦NTRHL CARO *) " """ ~ " QKRG2S20

2000 STOP AK?_G?_8*P

QKRG2B60

289

QIKREG SAMPLE OUTPUT

- kss sr

— - if4f|lflC4l 4RMM1I-

if tHotin nmifioH of i •

114*0440 0(414710* Of ■ »

ii, n m

VMNIIO

crwM|ti(*t n* oitiiHlHit ion • o.imio

CflMLUmOB Catf^iCJtJlT i J.rtiU-

cwr.iifutitiwi

• MIDU41S PRO* RfCRfMlOH

OMIRMO »UWf C0HMJt(0 U*

9 «K 1

•tilouii

9-t m

7189,000

■7.000

•7,17*

-9.57*

| 41H4HM4

7*71.000

41.000

47.171

7.079

I4H4MCI*

41?6.000

100.000

112.049

-12.099

I 4RC40I6

4**1.000

*1.000

00.999

-17.551

t !••«• MflLt

1124.000 . . .

. . . 22.000

76. *(9

9-917

1041 OHIH (Ml .

*81*. 090

• 7.000

•9.5*7

1.491

IMlirLOWR

*174.000

•1.000

•0.719

0.269

(OCMtttV

l 147 7. 000

122. 900

114.114

-17.616

IOCVMIT HU1 1

7110.000

41.000

40.4J7

1.009

IMM 7-H

7*1 7. r JO

•7,000

41,410

-4.410

1 OMR 04 44

11 _

*964. 6V9

100,000

•9.014

_ 14,401

1 ORJA.4 V1IT4

. 1

6714.000

•0.000

77.2*6

2.79*

ICOHOTOH

7121.090

4*. ooo

#0.070

7.121

ICOHCORO

4711.900

46.000

•2.464

II. 01 I

IC0974 4C14

, 16 . .

5867.000

4J.OOO

94. 75*

-1.75*

icmvcr cm

1000. 900

104.000

96.214

7.761

10617 cm

•249.000

. _11 . 20 Q .

44 , 1 *•

. - rLIM

100MV

_ .1

7071.009

41,000

•1.116

9.414

ItL C4JOH

JO .

(1)5.000

40.900

47.4*4

. -7.9*9

til CCRRITO

.. »

66 06.000

71.000

• 1.062

-6.062

1 (UR (84

, 21

51*1.000

••.000

00.144

. 1*100

IfRfMOHT

4194.000

• 1. 990

75.649

-7.649

< PR (140

7493.000

4(.000

46,101

. _ -5.IU.

_ KUUfRTON.

77*1.900

44.600

49.419

0.569

IC44MR4

?6 ..

7*90.000

190,000

40. 769

9.757

ICARDtn UNI

7961.000

•1.099

41.445

-10.649

(UtHMlC

.?•

76*4.000

40.000

42. 109

-7.909

t 4MTMOHHC

•

77 04. OOO

_iUi».W9 _

TT64.000
74? 1 , OOD
7*00.000
7*07.000
6170,000
6IM.QCQ

711*7,000
•?89. 000
• | 9 | ,000

6117.000

6610.000

7111.000

7610.000

7166.000

97.000

.M-ooo _

62.000
. 4 j ,000
It*. OOO

46.000

71.000

. 7 1,-POO -
•6.000
1 06. 000

115. 000

61.000

74.000
• 4.000

81.000

108.000

17. Ill

77.-56?

41.616
«.4»r
41,141
61.J45
60.644
JH.229
•7.141
44.410
40.561
7». 54 7
•1.921
•4. 104
42.449

4.414

IHWHAOO

_-4*HJt JMUR7IHCT0R P*M*

1174.000

76.000

•H.OU

8171.000

104.000

102. *•♦ .

7019.000

49.000

09.921

6101,000

75.000

77,751

44 05.000

74.000

70.070

•9.000

•2.440

6471.000

76.000

T4.540

5? . ..

4V3I.O00

106.000

4210.000

•1.000

76.469

4422. 060.

•0.000

•4.907

7064.000

•6.000

•4.104

5*.

5599.000

. 76,000

I0.699.

6*60.000

71.000

•1.450

48*0.000

41.000

. . •9,0*4

-1.604
-4.614
21.102
9, Til
-7.644

-1.561

16.694
-11.147
-2.119
-9.104
-7.649
... »*.**!

6.104
... 1.410

4.474

11404.(4000
til N6066

U64 mono
no

HOMO 006CM

_L1A.

UVHtOOO
(46*0*4 7 77 4 M6CH
IHOHIO OMR
1NOMST0
(MOHR (74 1 4
IHOHTtmiO
(MOHTCRCV MU
1 67 VICH

<MiM0M6i cm

..«9C0njH7 •••o*.
M44.K

I0H6HM

(0XH6R0

10*10 6.170 .

6411,000

“•7“

6807.000

6461.000

7015.000

6121.000
746*9. 000

7104.000

4614.000

4717.000
*6944.000

7110. 000
"•714.000*

4104.000

44M.M6

7477.000

9247. 000

6149.000
"6947.000

4147.000

f 0.000

•7.000

72.000

74.000

64.000

*01.090

77.000

iHIS- —

“65.OO0

n.OOO

40.000

41.000

no: ooo

11.000

"46.060“

40.000

67.000

41.000

74.000
74.000

06.714

09.714
79.910
49.050
•4. 591
•1.144“
02.272 .
06.001
00.415
40. 612
77.764

T4.4M"

40.901

60.797

•9.007

"00.906

xsi — ««*—

*.*IP

-9.940
. -l ^o
0.097

_Lf %46ff *U.

1.041 IRICO 0IV044

... rWJI ..WP«4

-10.090 IICHMOS

. .6..*W JMJQHM MICH. ...

9.477 IMMOOT CIT7

-12.794 ffOCOMHHTO

- ““ lfailM9

If AH Ml MAR 01 HO .

* IUH MUM

tog ogMrwyi

-0.794 "

-O.tll

5.144"*

-12.4*

I. Hi

9.144

4.069

"iV.'ioo"

4SS-S

. I 01 CM ~
...!»■ POfUiC.ffCf..
ItAH JOtl

146004716

■i.'C> -HaSrShro

**.609

-6.900

-HflR-l

Mti.boo

0094.000

7497.000 '
8050,900

oobo. boo
•iio. ooo

-*«f-

-Jtf-.Bf..

11.020

-19.002

.JLIWWTM

IIHHimi

-msf

4!iS!l!iiTii

64*17660

..77*?f000..

49.060

95.000
107.000

40.000

00.000

111, ooo

41.091

...79f04f.

49.572

42.000

•4,000..

0.410

iiltU

0.094

...99,*?*. .

IWM.ttJJIfL A..

2S6

CS 290

THE COMPUTE! IN UNDERGRADUATE GEOGRAPHY AT HIDDLEBU RY

Vincent H. Halnstron
Hiddlebury College
Hiddlebury, Vernont 05753
Telephone: (802) 386-4051

The use of the computer 1l the processing and graphic presentation of geographic data is
not only a sell- established practice today, it is also one of rapidly growing importance. Many
research projects which were scarcely conceivable in the years B. C. ("before the conputer") are
now coiuoplace, though one would besita^ to cali. then routine. Horeover, the availability of
sophisticated programs such as SYBAP and SYBVU pernit the graphic portrayal of in ornation of
interest to the geographer so readily and so effectively that whole new dineneions of
cartography are being opened. Thus far, however, as is to be expected, the principal utilization
of this exciting tool has been at the graduate and post-graduate levels of research and
teaching. Seldon is the undergraduate exposed to a conputer, except perhaps in sone gane-piaying
situation, and then usually in a fairly straight-forward g uestion-and-answer relationship. It is
the author's belief, however, that the undergraduate student should becone acquainted with this
powerful tool as soon as possible in his acadenic career and that he should do this, insofar as
possible, by enploying it in research projects of his own design. With these goals in nind, the
author has developed several prograns which have been used with considerable success in
introductory as well as advanced geography courses at Hiddlebury College.

It should be stressed at the outset, however, that the forn which undergraduate involvement
with the conputer has taken at Riddlebury is the direct result of the facilities available to
our students. Hiddlebury College very early joined the Dartn r ; th Tine-Sharing Systen and has
since enjoyed the naaifold capabilities which the Kiewit Computation Center affords. Anong the
nost obvious advantages of this association are: (1) the use of BASIC as the principal language,
allowing students with no previous conputer experience to successfully run prograns after only a
nininun of instruction; (2) a direct and instantaneous student contact with the conputer,
obviating the need for punching decks of cards, delivering then, and calling for the results
later; {when using the teletype and BASIC, the student is innediately informed of any fornat
errors he nay have nade, and after the appropriate corrections have boen undertaken, the running
of the program yields innediate results) ; ar* (3) because the College has contracted for
blocktine, the only constraint on the student-use the conputer is the availability of a
teletype console - in contrast to other situations where Units to use are inposed by financial
considerations. It is against this background, therefore, that the conputer experience in
undergraduate geography at Riddlebury nust be viewed.

In the introductory geography course, which averages between 180 and 220 students per
year, the first conputer assignment normally involves a clinatic analysis. For this purpose, a
classification systen recently developed by the author has been enployed. Indeed, the
classification itself was developed with the assistance of the conputer, and student research
projects have largely been geared to testing new data and verifying results with the system.
Knowledge of this fact has enhanced the students9 interest in and appreciation of the project,
which is not viewed as being sinply something to do as a course requirenent but as an endeavor
having broader professional and practical applications. After the student has called the progran
(entitled HACLIH) from the Dartmouth library, he inserts the appropriate data for his station
and is inforned in return of the Water Heed, the Warmth and Hoisture Indices of the station, and
its clinatic classification. (Having previously spent from 15 to 30 minutes manually working out
sinilar results, he is, of course, innensely inpressed to obtain the sane datar usually nore
accurately calculated, in a quarter of a second!) Boreover, the conputer then gives him the
option of having the water Balance of the station analyzed on a month- by- non th basis, and beyond
that, when the teletype is coupled to an HP-7000A plotter, of having the Water Budget graphed
out for bin. Using one or nore of these computer-generated naterials, the student is then called
upon to identify the clinatic station (if this infornation has not been previously provided for
hin) and to interpret the results in terrs of the land-use potential of the region, and the
availability of water for irrigation, power, etc. When the results of individual student
projects are later drawn together and conpared, broader regional differences in clinate are
quickly discovered and possible explanations are offered. In this nanner the student cones to
appreciate the conputer as a valuable analytical tool* in this instance for enhancing his
understanding of the variations through space of clinatic phenomena.

The geographer's concern with the spatial analysis of data is effectively illustrated by
yet another use of the conputer in our introductory course, namely in the production of 'maps*
whose content the student is called upon to interpret and explain. For this exercise, data not
commonly portrayed on conventional atlas naps are stored in a series of files, ten items to a
file. (For this reason alone the student is aware that he is creating an 'original* nap with the
help of the conputer.) In one recent exercise, for exanple, three such files were used for a
class of over 200 students, resulting in approxinately seven printouts for each set of data.

i ^2SH

2S7

Beca tk« assigssests vere rasdosl y ladt, there vas little likelihood of collaboration bttvMi
students working oa the save data# and. due to the independent aatare of tke assignees t# little
consequence of suck collaboration kad indeed takes place.

Before tke exercise itself is described sore fully, a word skoald be field a bo at tke ssppisg
progras upon vhich it is based. Developed by tke author is collaboration vitk sose of kis
advanced student*, tke so-called COBPBAP progras sake* so pretense of providing so sopkisticated
a product as tkat produced by ST SAP# for exasple. Xs its present fors# kovever# COBPflkP does
provide tke atedest vitk an opportunity to prepare kis ovs saps os a teletype printer, vitk all
the lisitatioss iskerent in suck a piece of hardvare# iscludisg nsrros sap forsat*# relatively
sloe printost# and a restricted ckoice of pristisg tones**. 4 song tke optioss opes to tke
student vitk tke COflPSkP progras are (1) tke spatial ordering of data# eitker is 9rav9 or
sanipulated fors (tke so-called "data-poist" sap) ; (2) the prodectios of a "ays bo la* sap# on
vhich squares proportional to tke data are dravn by a plotter; and (3) tke production of a
"choropleth" sap os vkick areas are skaded according to the classes of data vhich sack of tkes
represents. If tke user specifies the latter option# he kas tke furtker ckoice of having tke
data analysed by quartiles# quintiles# or by classes vkose intervals he say visk to specify
hisself# suck as 30k# 40k# etc. For tke first tvo kinds of saps# tvo files are osed, tke so-
called 4-File# vhich provides tke naves and coordinates of all tke places to be skovs os tke
•ap# and tke 8-File, vkich contains up to ten itens of data to be sapped for sack place. la tke
preparation of a choropleth sap# a third, or C-Pile# is required to outline tke areas to be
shaded.

Whether the student elects to produce a data-point# sysbol# or choropleth sap will depend
on the use he istesds to sake of it. While tke sysbol and choropleth saps both bare greater
visual ispact than the data-point sap# the latter cas be easily contoured asd likevise persits
further statistical analysis, Horeover# it is tke fastest to print out# and hence kas bees tke
type of sap sost frequently used in our beginning classes. (To cite a specific exaeple# a recast
exercise vkich sapped data for the 58 counties in the State of California averaged about 1/2
second of cosputer tise and took about 1 and 1/2 sinutes to print out.) Os the other kasd# as
upper-classsas vorking on a ters paper in a regional geography course used tke "sysbol a" option
to produce an urban atlas of tke entire Soviet Union. Ia it ke not only depicted every city over
100,000 population for each census fios 1897 on# but by a sisple saaipulation of tke data ke
also shoved tkeir absolute grovth during each istercessal period. Thus# by using tho C08FH4P
progras, he accosplished in a fev days9 tise vhat would have taken literally souths to do by
hand — and again# vitk far greater accuracy than if it kad been carried oat annually by a
cartographer. Thanks to tke cosputer# he had produced a valuable piece of original research#
vhich, vhen suitably edited and re-drafted# could conceivably fors the basis of a professional
paper of scse serit.

Getting back the cosputer sapping exercise in the large introductory coarse, once tke
student had prepared his data-point sap, kis assignsent van to explain the patterns ke found
using any other source saterials vkick be could uncover, flany of then looked for c] les in the
printouts of cosputer saps dealing vitk other# related subjects# as veil as is textual and
cartographic saterials available in tke library. 41sost vitkout exception# tke students
experienced a real 9 involvesest 9 vith their respective projects# bringing to bear ia tkeir
analyses virtually all the principles that kad bees discussed through tke ters. Indeed# sany of
thes turned in highly perceptive studies# accospanied by finished saps vkich vere based oa tke
cosputer data.

Although tke challenges confronting
the 9 teletype cartographer9 are
sosevkat akin to those vhich tke losans
faced in using rolls of papyrus,
saps of any vidtk can be produced by
pasting the strips together.

klthougk over-printing is possible for
espkasizing tonal differences# *ts use
greatly slovs dovn an already slov printout

In the illustrations cited above, the use of the coaputer has provided the undergraduate
student with critical assistance in solving problems within the context of our regular geography
curriculum. However, a far more ambitious computer-oriented course was developed and offered by
the author during the Winter Tern of 1972. (During this five-week period, the stadent
concentrates on a single course of study.) Entitled MWorld 2000, " this course was limited to an
enrollment of 20. By drawing lots, each student was assigned to represent one of the twenty most
populous nations in the worJ a. Although the size of the country's population was the chief
criterion for including it in the list, it was felt that they would provide a wide range of
diversity in levels of econonic development as well, ranging from the United States and the
Soviet Union at one extreme to China and India on the other. After completing a 'national
inventory9 for each of the countries by collecting statistical data on virtually all aspects of
its econonic, social, and political life, the students utililized the computer to manipulate
these data for purposes of projection and analysis. For efkmple, using the clisate
classification described earlier as a basis, they ran a program called WEATHEB to determine
whether their crop yields would be up or down from one year to the next. Inasmuch as each class
day was intended to represent a one-year projection into the future, when the students cane to
class each day, the weather summary for the preceding 9year9 for a representative station in
their country was ready for their analysis*, having already run another program titled F08CAST
to determine what his grain (and other commodity) needs would be, both at existing (i.e. 1971)
and improved levels of consumption — the student would quickly ascertain whether his harvest
would be adeguate to meet his own requirements or by how great a margin it fell short of or
exceeded these needs, thereby necessitating imports or permitting exports. This in turn would
engaqe his country in interaction with other countries through the medium of trade, for which
another program (by that name) was available for 'bookkeeping9 purposes. Another program
entitled BUDGET established the financial resources available to each country and provided each
flayer with the option to budget then as he saw fit. Yet other programs provided a
quantification of the effectiveness of given policies instituted by the different governments
and an annual overview of the internal and external political situations. Likewise, each "year"
the players ran a program entitled SUHHABY to take stock of theit government's economic and
political progress during the preceding 'twelve months.9 Positive achievements were registered
in increased GNP's aad per capita incomes, and in the increased support of the people, whereas
stagnation or regression was reflected in an eroding economy and political disaffection. As the
plight of some countries became increasingly desperate with time, they called for the option of
using force in their dealings with one another, and asked that a WAB program be created a
request which necessarily was met but with some hesitance and regret.

Naturally, the outcome of such a course is strongly dictated by the personalities and
decisions of the individual players, as indeed, is the course of human events in the real world.
No doubt very different results would have been forthcoming had twenty other students played
each of the respective roles, or even if the sane twenty students had each represented a
different country. Nevertheless, at the termination of the course, all were agreed that it had
provided an incomparable learning experience, not only giving then a far greater understanding
of the major problems confronting the nations of the world today, but also a much deeper
appreciation of how individual, momentary decisions materially affect long-term results.
Everyone likewise came away from the course cognizant of the central role the computer had
played in it, not only as a 'purveyor of facts' on which to base decisions, but also as a
dispassionate 'judge' of such varied conditions as the quality of the environment in an
industrialized nation to the severity of malnutrition in an underdeveloped country. Indeed, it
should be emphasized that the design and execution of this winter tern course would have been
quite inpossible without the computer, with which a teletype link was kept open for the entire 2
1/2 hour class period each day in order to expedite decisions and interactions. Thus, from
having successfully involved students in using the computer for individual research projects as
outside assignnemts in courses regularly offered in the fall and spring terns, the author feels
that he has made a large and rewarding advance toward structuring an entire course around its
use during the shorter winter tern. On the basis of the favorable response of the students, and
with an increased neasure of "wisdom" born of this experience, he confidently anticipates the
expanded iso of a "coipu ter-orientod approach" in his regular course offering? in the future.

* Here, actual data was used from a

series of years in the past. Obviously,
no student was allowed "advanced warning"
of any oscillation in the climate, but
was obliged to adapt 'after the fact.'

zzs

293

THE USE OP CQI1PUTBBS lh GEOGRAPHIC INSTEUCTION
XS A n RAN ^ FOR

STIHUL ATING INTEREST IN STATISTICAL METHODS

David J. coven and Paul E. Loviogood, dr.
University of South Carolina
Coluibia, South Carolina 29206
Telephone: (303) 777-5234

A iajor problem confronting anyone teaching a required undergraduate statistics course to
students in the social sciences is overcoming the apathy concerning the subject natter. In
teaching such a course to undergraduate geography najors for the past tvo years, ve have found
that by having the students actually collect their ovn set of data and analyze it vith the ai.'
of the computer# interest has been stimulated and the student has attained a sense of
accomplishment. The purpose of this paper is to discuss some of the specific vay£, ve have
utilized the computer in overconing the apathy of the stuuc*ats to statistics.

In order to create interest and a sense of self-confidence each student in the first week
of class is required to collect a set of his ovn data. Because this is a course in geography the
observation units must be geographical areas such as counties, cities# or states. For each of
the observations five or six variables are assembled into a data matrix. It should oe noted that
the students are encouraged to collect daca for the local region or the state. The student is
therefore familiar vith the data and interested in the findings. The student is instructed in
data coding and keypunch operation. After punching his data he runs simple canned reproduction
and data description programs. Ve have found that the student reacts veil to this initial
assignment and enjoys getting his first computer printouts. It also is helpful vhen covering
measures of central tendency and variance for the student to have his ovn printouts vith him in
class. In addition, the printout provides a check for him vhen vorking out computations on a
desk calculator.

This year in conjunction vith the statistics course ve ran a non-credit FORTRAN programming
course for students in the department. Ve found that in five or si x sessions the student could
learn to vrite his ovn program for computing some of the simple descriptive statistics. The
students vho diligently participated in the programming course developed a better comprehension
of the statistical methods. It vas especially useful to relate programming statements to the
corresponding mathematical procedures.

In discussions of data displays ve have utilized a canned histogram program as demonstrated
in Figure 1. The printout is utilized as an aid to the student in preparing his ova displays.

FIGURE 1.

NUMBER Of PHYSICIANS PER ONE THOUSAND POPULATION IN S.C., 1970
TABLE CF 46 ITEMS COUNTED INTO CELLS
TABLE OF 5 ITEMS COUNTED INTO CELLS

EACH ASTERISK IN A CELL WALL REPRESENTS A COUNT OF 1
NO. CENTER COUNT HISTOGRAM

0.2

♦

•

0.6

•

► *. 3

1 .0

•

1.4

+ •

♦#

1 .8

♦ #

« *

PREPARED BY MICHAEL TREADWELL FOR GEOGRAPHY 53li FALL 1971
UNIVERSITY OF SOUTH CAROLINA

In geography point distributions are significant. Therefore, we spend a few lectures
dealing with quantitative analysis of these dirtributioa* on naps. At this tiae the student
collects another set of data pertaining to the spatial distribution of sone phenonenon such as
playgrounds, grocery ntoren, or banks, ye in then introduced to cartesian coordinates and runs a
progran that generates nearest neighbor and bivariate descriptive statistics. Based on this
output the student writes a short paper in which he discusses the distribution of the phenonenon
and interprets the inplic^tions of his findings.

The last part of the course is devoted to analysis of variance and sinple linear regression
aodeis. The student develops his own hypotheses pertaining to regional differences between areas
in his study region. For exanple, a certain group or region of counties night be expected to
differ significantly fron another vith respect to certain socio-econonic variables. In the case
of South Carolina nany of these regional differences portain to urban versus rural or piednont
versus coastal plain counties. The hypothesized regional differences are exanined by the student
with the ad of a canned analysis of variance progran. As in all exercises the student is
introduced to the nethod in class and works out his own results on the desk calculator to gain a
better understanding. The coaputer output serves as a check on his own calculations.

The discussion of regression usually proves to be of nost interest to the student. He
usually has assenbled his initial data set with the idea * exanining the relationship between
••wo socio-economic variables such as racial nix and ncone level. Sone students originally
gather their set of data rapidly and without nuch thought and therefore decide to collect nore
neaningful data for this section. Although the theoretical structure of statistical hypothesis
testing is stressed in class, extensive developnent of the hypothesized relationship is not
deenea necessary for this exercise. The output fron a regression progran serves as an inportant
teaching aid in the discussion of estinating paraneters for the least squares regression line
and variance explanation.

As a final assignnent the students nap two of the variables and exaniae the pattern of
residuals fron the regression line, we have developed several conputer napping routines for the
local area to aid in this final project. To undergraduate geography students producing and
seeing their own data napped by a conputer prjves to be quite exciting. Figures 2, 3, and 4 are
exanples of such naps produced by a student who is interested in the relationship between the
distribution of physicians and urbanization within the state of South Caroline, Sone of the
students who worked through the F0BT8AN course have beon developing their own base naps.
However, we have found it nore efficient to let nost students use our existing prog ra ns.

FIGURE 2.

NUUBErt OF PHYSICIANS PER UnE ThOUSANO POPULATION IN S.C.. 1970

PREPARED BY MICHAEL TREAC L FOR GEOGRAPHY 531. FALL 1971

university j. south Carolina

FIGURE 3.

UMAX POPULATION as A PERCENT OF TOTAL POP UL A T 1 ON . BY COUNTIES* IN J.C. * H TO

FIGURE 4.

FE AGENT UMAX POPULATION ON HUPB£* OF PHYSIC! ASS/VOOO POPULATION
ST ANOAAO 1 2E 0 AESIOUALS FkON AEGAESSION. BY COUNTY - S.C. 1970

PAEPAAEO BY MICHAEL TAEAOMELL FOA GEOGRAPHY $31* FALL 1971
UNIVERSITY OF SOUTH CAROLINA

It the conclusion of this course the student has actually coa plated a . sail piece of his
own research. Instead of working out a set of prearranged exercises fron data s spiled to hin
he ’.ii collected and analyzed his own* By introducing then to the computer and its capabilities
at the outset of the course the students gain a sense of adventure and apathy towards
statistics is reduced* In addition, the coaputer output is essential in this type of course as
an instructional tool and as a aeans for students to check their own exercises*

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302

I NTBODUCING UND2RGB ADUATE GEGGBAP/JERS TO QUANTITATIVE
ANALYSIS THROUGH A REGIONAL I 2 ATI ON FRAHEWOBK

Nancy B. Hultguist
University of Iowa
Iowa City, Iona 52240
Telephone: (319) 353-3131

Introduction

Analysis of spatially recorded data by leans of statistical and aatheaatical techniques
has becone firnly established in geographic research with the coaputer as a necessary tool.
Puture professional geographers need to be prepared# therefore# to handle quantitative nethods.
Por this reason# courses in quantitative geography appear in the curricula of aany graduate
prograas in a variety of foras varying froa straightforward descriptive aeasures through
inferential statistics to advanced aultivariate analysis# and aost students who continue into
qraduate wort are required to naster quantitative techniques. Undergraduate teachers# however#
have been slow to introduce such techniques# perhaps aainly because oi: their lack of technical
training. Consequently# aany undergraduates are not introduced either to quantitative
aethodology or to coaputer techniques. Por aany the adjustaent to quamti tati ve analysis at the
graduate level is often trauaatic. Therefore# it is proposed here that a survey of techniques
of quantitative analysis and the tools for aanipulating and displaying data should be introduced
early in the student*s career.

The objective of this paper is to exanine an experiaental course which was offered in the
Departaent of Geography at Georgia State University in 1970 solely for undergraduates# not
necessarily aajors. The course# "Techniques of Spatial Quantification"# introduced selected
statistical techniques aost often encountered in the geographic literature and encouraged
coaputer usage and interpretation of results. It was offered during the fall and spring
quarters. Purposefully# the course did not dwell on aatheaatical particulars of each technique
introduced but presented an intuitive explanation related priaarily to application. One
objective of the course was to reaove fear of statistics and coaputers# and at the sane tine to
deaonstrate their value as tools in spatially-oriented research. While it is possible to teach
a basic statistics course without using the coaputer# a course of the type described here aust
concentrate on coaputer involveaent sinpiy because of the scope. It is recoaaended that such a
course should be incorporated into all undergraduate departments# limited to aajors if necessary
to control enrollaent.

Data Provided for Bach Student

The aeabers of the class were divided into four groups# each of which dealt with one
particular region consisting of forty Georgia counties contiguously grouped froa north to south
(see Figure 1). Because there are 159 counties# necessarily there was one overlapping county
(Gwinnett). The data for each county consisted of 45 census variables# 20 of which were
percentage data used for aost analyses (see Table 1) • Bach student had his own data deck. This
provided the basis for problem exercises and for class discussion of techniques. The regions
were relatively faniliar to the students and were therefore conducive to a neaningful analysis
of the data and of the statistical techniques introduced.

of £Usa

For the first foar weeks# the class consisted of five lectures per week. During this tine
an historical developaent of the use of quantitative nethods in geography, of aatheaatical and
statistical terainology# and of basic statistics were presented. Thereafter# the course assuned
a seainar-labora tory orientation. Progran runs were distributed. New techniques were discussed#
probleas ironed out# or interesting findings discussed.

The course instruction assuned no knowledge of the coaputer and# in aost cases# the
students had no prior experience with prograaaing. The introduction involved basic coaputer
terainology# concepts# and use of peripheral equipaent. While prograaaing per S£ was not taught#
certain FOHTBAH specifics were introduced# including foraat statements, variable node# and
coluanar specifications as would be encountered in aaking control cards for a library progran.
Several short prograas were written in class by the instructor to indicate the type of
aanipulations possible in FOHTBAN. The students were encouraged to keypunch one of these and run
it with hypothetical data.

- ' : ? I r

304:

ERLC

300

TABLE 1

LIST OF VABIABLES
A

1. population per square mile

2. x percentage population change 1950-60

3. percent urban 1960

4. percent Black 1960

5. ratio of <brtcths to deaths

6 median school years coipleted for persons over 25 in I960

7. per capita income

8. median faaily incoae in 1959 of fanilies in 1960

9. percent families earning under $3,000

10. percent families earning over $10,000

11. percent all land in farms (1959)

12. percent all commercial farms with sales over $10,000

13. total persons in farm operated households

14. total employment

15. percent enployaent in agriculture

16. percent employment in forestry aud fishing

17. percent employment in construction

18. percent enployaent in manufacturing

19. percent enployaent in wholesale and retail trade

20. percent employment in services

Other programs used were arranged so that multiple data decks could be submitted
simultaneously on one computer run producing an individually identified print-out for each
student. The laboratory sessions were used to examine the results and to discuss regional
differences displayed by the different print-outs. Students mere held responsible for furnishing
control cards for each prograa, usually consisting of an identification card, parameter card (s) ,
and a variable format card.

Over a throe-month period, many tests, techniques, and grouping procedures were examined by
the students, including measures of central tendency and dispersion, normality and
transformations, correlation and regression analysis, principal components analysis, and
discriminant analysis.

Students were required to run their entire data deck through each program introduced, and
were encouraged to make special runs to follow up hypotheses by deleting observations or
variables. Since the master program read in each student’s deck as data, often one student’s

301

305

error would ruin
neophytes gained

the day*s run tor his clasanates. This
■ore respect for careful keypunching and

happened only
verification.

fen tines as the

canned Programs Utilised

The first progran run was a sinple FORTRAN progran producing naans, standard deviations,
standard scores, a correlation table, and reciprocal pairs of highest correlations. Horn tine
was spent on analyzing this progran than any other throughout the course, because nany basics
were involved. Students chose variables of interest and napped their standard scores. This
provided a feeling for the counties in their study area# for eianple, rich vs. poor, urban vs.
rural, population growth counties, educational levels, and enploynent patterns. Students were
encouraged to do sone supplemental research to substantiate quantitative findings.

After discussing the variables in relation to the counties, students ezanined the
relationships existing anong the variables. Positive and negative correlations with each
variable were listed. An iaportant subset of this list, a listing of variables with highest
correlations and reciprocal pairs, was provided by the conputer progran. Pron this output a
linkage analysis was performed [1]. Students were able to note the iaportant linkages anong
variables over all counties, thus giving an even better picture of the characteristics in each
area. At this point students had no way of napping these findings precisely, but at least they
were able to generalize linkages and to forn sone hypotheses which could be verified with later
techniques.

The next progran introduced involved an hierarchical grouping routine written by Donald
Veldnan[2], This progran standardizes data natrices and groups observations (or variables) using
generalized distance functions to nininize total within-group variance at each step in the
process. Students can nap groups at various stages of the process and fornulate hypotheses about
the reasons for these groupings. Sone students found it interesting to use variables which
conbined on one of the najor links noted in the previous progran. The heirarchical grouping
progran is helpful in pointing out counties tthich are "similar" with respect to the variables,
and in allowing experimentation with variables to see how groupings change.

A multiple discriminant analysis progran *as introduced which allowed students to check out
sone of their hypotheses about appropriate homogeneous groupings based on any selected
variables. The output indicated the statistical validity of their choices. Students were often
temporarily shocked that the conputer caught something they had overlooked, but upon
reflection, they siaply becaae nore avid conputer users. That was not always the case, however.
Sone students preferred the subjectivity they could inpart to the situation.

Principal components analysis with varisax rotation was introduced next. Hot surprisingly,
the factors usually indicated dimensions sinilar to the linkage analysis results, except for a
bi-polar factor which absorbed two linkages. The concepts for factor analytic interpretations
were easily accepted because of the forner work with linkage analysis.

Various graphic techniques were used to display the conputer results, but because of lack
of conputer equipment, these were done by hand. More sophisticated equipment such as line
plotters, cathode- ray tubes, or software such as SYflAP or flAPIT could be used with larger
installations. At the tine of this course, the available conputer was an IBH 7040 with no
plotter and with linited terminals. Students determined the high positive and negative factor
loadings (.500 and above) and then naned the factors. They graphed factors against one another
and labeled counties, e.g. rural vs. urban. Pactor scores were presented by the progran. They
were graphed, napped, and interpreted further.

Results of the Course

◦ne measure of course success cane in the students9 final report on activities taken to
quantitatively describe their areas of Georgia. The reports indicate that a great anount of
interest and work took place throughout the quarter. In addition to individual reports, each
group of students also gave a resune of their findings to the entire class. This gave everyone
the chance to see Georgia altogether for a change.

Another successful note was the interest generated, persons fron the fall quarter enrolled
in an urban geography course the following quarter and chose topics which utilized conputer
techniques. There was also enough interest generated that during the spring quarter the course
was offered again, and an additional advanced course was taught for sone of the original nenbers
of the fall group. In the advanced class each person learned nore FORTRAN# tackled a research
topic of particular interest to hin, and learned additional techniques.

ERIC

3C6

Conclusions

Apparently, the addition of computers to the quantitative geography course ottering was
useful for at least two reasons. Sore iaportaatly, it introduced the stadeot to current
techniques of research in the field and to terniaology with vhich he needed to becoae faailiar.
Secondly, the personal use of the conputer gave undergraduates an interest in the course and
provided a necessity for keeping up-to-date on assignaents. In this case conputer tine and aoney
were not prcblens. with current financial limitations in sone universities, the sane course
night still be taught with group rather than individual involvenent. There is no doubt, hovever,
that the individual responsibility for conputer runs is a preferable situation and will produce
favorable results.

REFERENCES

1. HcQuitty, Louis L. (1957), "Elementary Linkage Analysis for Isolating Orthogonal and

Oblique Types and Typal Relevancies, " Education qqd Psychological Measurement, Vol.
17, pp. 207-229.

2. Veldnan, Donald, Fortran Programming for tfce Behavioral Science, (1967), Nev York: Holt,

Rinehart, and Winston, pp. 308-317.

303

3C7

CAI AND ENGLISH: A TENTATIVE fi ELATI ONS HIP

Anna Marie Thanes
Golden Nest College
Huntington Beach, California 92647
Telephone: (714) 892-7711

Computer programs written for remedial English students at Golden West College are designed
for a specific coarse, English B. It is prerequisite for the college transfer English course
and is required for those students who fail the college entrance test and a. paragraph writing
challenge* The students neet this class only twice a week for discussion and paragraph writing.
In ny classes the students are expected to spend at least one hour per week, for nine weeks,
working on conputer-progranned exercises in spelling, diction, sentence structure and paragraph
construction.

The student who takes this course does so because he failed to pass an entrance examination
which would have qualified bin for the transfer composition course, and who subsequently
enrolled for and failed English A, a grammar review. Subsequent to passing English A, he then
failed to pass a challenge exam consisting of one paragraph he was asked to write. In passing
this exam he could have bypassed English B. Therefore, he has failed at least twice at the
college level to reach the goal of writing an effective paragraph.

Very often sQch a student does not have a high school diploma or has failed English in high
school as well. After failing the second college challenge exam, he is scheduled to attend
this class for nine weeks; his primary goal is to write a paragraph of approximately seventy-
five to a hundred words which is unified, logical, and substantial.

From the beginning, the course seemed difficult to teach because, in -^pite of ny
assuuptions about these students, their abilities varied greatly. They had one inability in
common, however; they could not write a paragraph. After two semesters of frustrating
experiences, I decided to develop other means of teaching the course, using the computer to meet
individual problems, since the college did not provide tutors. In April, 1969, I asked one of ny
former students (who was fortunately a much better programmer than an English student) if he
would teach fle how to write programs for remedial English. fiesearch suggested that little was
known about the capability of the computer for use in teaching English: so the first step was to
write an experimental exercise in API.. In the summer of 1969, on a Project SAL (Systems Approach
to Learning) grant, we began to develop programs which would stress the principles of paragraph
writing, such as unity and coherence, through drill and practice as well as programs which
focused on special problems in diction. Vie worked beyond the summer project until November,
designing about 20 programs, written for students who were ready to begin the nine-week course.
At the end of that semester about half the programs were dropped, either because they were
poorly designed or incompatible with the restrictions of the computer. Por the last two years,
the remaining programs (about 10), as well as a few new ones, have been continually revised — a
critical advantage, incidentally, of CAI over programmed texts. The rationale for using the
computer was based on these assumptions:

1. Students can be motivated if they are active rather than passive participants in the

learning process.

Using a computer is a positive rather than a negative experience

The text of the programs and responses should be entertaining as well as informative

4. A few elementary programs used by students would point a direction for more
sophisticated and ambitious programs later.

Manipulation of writing segments can make a student aware of his own weaknesses in
writing.

The results were these general goals:

1. To individualize specific segments of writing skills instruction.

2. To reach the student at bis level of performance.

3. To provide an immediate and re-enforcing kind of response to his efforts

4. To shift the responsibility of learning from teacher to student.

To move mechanical aspects of the course out of the classrooa to sake rooi for
discussion of style, viewpoint, and writing.

To reiove the pressure of grades (by requiring only that students coaplete prograas).

The descriptions which follow include only those prograas which have been tested throughout
the past three seaesters by approximately 600 students.

CONFUSBD is a program which asks students to distinguish between often-confused words;
e.g., then-than, who#s-whose, its-it*s. The student is asked to type in a blank one of two words
which is appropriate to the sentence. If he is correct, no explanation is given; he is presented
with the next sentence. For incorrect responses, he is given a definition of each word,
("affect" and "effect," for example) and then directed to one additional sentence reguiring the
sane words. Only ten sentences are presented if he answers them correctly, thirty if he answers
then all incorrectly.

SPELLING is the naae of a program which types a sentence and then asks the student to find
within it a misspelled word. In the first segment of this program, the correct answers are
calculated, and the words which he missed are typed out. Then he is directed to another program
which includes rules for spelling certain categories of words, and requires practice in using
then.

TOPSRN is a program which includes three different exercises. The first, called SPECIFY,
presents a statement which the student is asked to label "5" (specific) or MG" (generalization).
For each wrong answer, he is given an explanation. No score is tallied. In the second exercise,
SCRAMBLE, he is presented with a paragraph whose sentences are listed in the wrong order. He is
asked to identify the topic sentence of the paragraph. In the third exercise, SELECT, three
sentences are typed out and the student is asked to select the one which could best be developed
into a single paragraph. Neither of the last two programs include individual responses to wrojig
answers.

UNITY is, for the alert student, a rather short exercise since he need only answer the
first two questions correctly to coaplete the program. Be is presented with a paragraph,
including one or wore sentences which do not support the topic sentence. He is asked to
identify then. This is an elaborately designed program in the sense that all possible responses
are anticipated. If either of his first two answers is incorrect, he is presented with shorter
less complex paragraphs.

PAHACO is a program which operates on the same design — the student is presented with a
scrambled paragraph and be is asked to reorder it so that each sentence leads logically to the
next. Few students are successful with the most difficult paragraphs in this exercise. (A sample
student printout is included in the appendix.)

LINES includes two exercises. The first asks the student to find transitions included in
the paragraphs presented. Qis answers are scored, but individual branches are not included for
all possible wrong answers. The second program presents a paragraph with blanks which are to be
filled in from a library of pronouns. For each wrong answer, a rule is presented explaining the
reason for the correct pronoun. The second program also presents sentences with blanks to be
filled in from a library of transitions.

SUBCO is one of the few manipulative programs. The student is given a complex sentence, for
example, and asked to revise it as a compound sentence, using specific editing commands. Several
months went into the development of these commands so that they would be written in the language
or the student and would enable the text to be manipulated rapidly. If, for example, the student
is asked to change the compound sentence: "He doesn’t like her, but I do," to a complex
sentence, he can respond with the following commands:

This is a rather complicated program for the student, since he must use the right commands,
manipulate phrases, and spell correctly. It was more complicated for the programmer, since he
had to account in the program for mechanical errors as well as a variety of correct choices the
student might Bake. (See appendix for samples of student copy for this program.)

INSERT EVEN THOUGH BEFORE HE

DROP BUT,

the computer would then type back:

EVEN THOUGH HE DOES N • T LIKE HER, I DO

Id MODIFIERS, the student is again manipulating teit and directing the computer. Because of
his experience in SUBCO and the interest level cf text here, student response is fairly
positive. (See appendix for sample of student copy.)

In HISMQD, the student is asked to identify aisplaced aodifiers and aove thea. For example,
in the sentence

BEEB SHOULD NOT BE SOLD TO STUDENTS CONTAINING ROBE THAN 3.2% ALCOHOL,
the student is first asked to identify the modifier, typing its first and last word,

CONTAINING ALCOHOL

If he does not identify this correctly, the coaputer will give it to hia. In any case, he is
next asked to re-locate it in the sentence using a caret (a) as an insert nark, in this fashion

BEER £

Wherever he places the caret, the coaputer will there insert the aodifier already identified:

BEER CONTAINING KOBE THAN 3.2% ALCOHOL SHOULD NOT BE SOLD TO STUDENTS

At this point, his revision is evaluated, and if he is incorrect, he is asked to try again. This
continues for a total of three sentences.

WORDYMOD prints sentences which are obviously wordy, and the student is asked to delete all
unnecessary words. He aust use editing coaaands to accoaplish this. For exaapie, in the phrase,

TWO CHARACTEBISTICS 6 HICH ABE NECESSARY FOB GOOD S ALESMANSHIP,

the student would type

DROP WHICH ABE

and then whatever other changes he wished to Bake in the rest of the sentence. The coaputer
would type back whatever changes he aade, right or wrong, as soon as he typed DONE. However, the
prograa does not allow for partial answers, and this is soaetiaes frustrating. By the tiae you
read this, he aay be getting credit for one change when several are prograaaed.

PREEHOD is a different workspace from the other two programs, so the student must load it
hiaseif. This aay be the prograa to delete if you are pressed for tiae. It involves a list of
sentences (a) which the student is asked to coapiete with one or two free aodifiers. For
exaapie, he is given the sentence:

IT RAY BE SAID THAT POLICEMEN ABE BATHEB SPECIAL, ALMOST ALIEN CREATURES
He is then asked to add a free aodifier, in this case
WITHIN THE AMERICAN SCENE
which he can insert, using a caret
CBEATUBESa

Obviously there is aore than one place in the sentence for this aodifier, so there are no
absolutely right answers. But the progran disallows ail answers than those designed. You aay
want to add aore. Only two placeaents are allowed for this sentence.

CBEATURES,a ait

This prograa requires about 30 minutes1 effort.

REVISE is the aost sophisticated prograa in this group and will soon undergo major
revision. The student is asked to write a paragraph constructed in this specific fora: a topic
sentence, three or aore aajor supporting) sentences, and three or aore minor supporting
sentences. Actually, he can skip any of the supporting sentences by pressing the return key on
the terminal. Once he has finished, the coaputer will /type the sentences in outline fora and ask
tor additions or deletions. At this point, the student can make word changes easily through
coaaands such as “replace** and "delete." Once he has coapleted his changes, the paragraph is
typed out in revised fora.

**07

3io

How the Pro qraws A^e Used

The programs are an integral part of the course. Each one is the subject of a week's
discussion in class. A handout is prepared which introduces a particular writing principle, such
as coherence, followed by various exaaples illustrating its application. At the conclusion of
the handout, the computer program is introduced, itr objectives are presented, and the student
is told how to sign on to it. The prograas are occasionally used as individual answers to
specific probleas of students in other courses.

Several prograas (not listed here) focus specifically on graaaatical probleas not discussed
in class, such as sentence fragaents and the over-use of the passive voice. Por exaaple, one
prograa asks the student to type a paragraph without any fora of the verb "to be." While the
prograa is very eleaentary in design, it does serve to prod the student who has this problea,
but nay ne unaware of it.

Student Reaction

Student reaction spans the distance between extrenely negative and obviously flattering
responses. Among those who offer criticism, t e brighter students are generally skeptical,
sometiaes reactionary, but frequently accurate in their consents. For eianple, they point out
that some of the prograas are written to accommodate the computer systea rather than the
student. Those who are less alert often complain about the complexity of the programs and the
precision required to complete thea successfully. These students have difficulty understanding
the directions. Within this group, some of the serious students seen to value the effort Bade to
reach them at their own ability level and the de-emphasis of competition. Within both groups,
there are some who enjoy the opportunity to work independently. Host complain that the course is
more difficult because of the computer prograas — they cannot sit passively, as in the classrooa,
responding only when they wish.

Nevertheless, he students coaplete the prograas, a requirement for passing the course, and
in so doing are forced to become involved actively. Those who stay in the course improve, both
in their ability to read and follow directions precisely, and to write an organized paragraph
concisely. And though they have failed college work in English at least twice (these students
frequently have a history of failure outside English courses as well) , aany are encouraged by
the discovery that they are capable of interacting with a computer.

Several student paragraphs are included here, unedited, because they represent the range as
well as the degree of criticisa encountered thus far.

Boland Clark: I am sure the computer prograa I enjoyed the aost was the first prograa £ used.

To be sure, having a typewriter talk back to Be, and answer ay questions was
very aaazing. One thing I like about the computers is when I answer a question
wrong X an not embarrassed to death. Oh I get eabarrassed all right, but I know
the computer doesn't aind so it's sort of personal. All 1 do is try to get the
coaputer programs, even if sone take aore tiae than they're worth.

Boger T. Brown: The computer is the unreachable instructor that will not take any backtalk from

its students. If anything is typed that is not asked for, such as a smart
coaeback to a question, the coaputer just writes — incorrect coaaand. There you
sit with the coaputer having the last word. It only wants to hear what it has
asked for and nothing else will do. I was once told that man is the only thing
on this planet that can reason. After using his God given reasoning ability, ae
turns around and asks a computer if he is right.

Tom Beason: 1 chose to evaluate a coaputer on the basis of its relationship to man. After

all the work, money, and training of personnel have gone into it, this "brain"
comes out an extremely useful tool to nan; always logical, never in error (if
in good mechanical repair), and able to give nearly instantaneous answers. But,
as a thinker, the computer is fast, efficient, and stupid; man is slow, cluasy
and brilliant.

Cynthia Bakkelo: Learning with the computer is sometiaes frustrating; yet it is a whole new way
of learning with individual attention. It takes tiae to adjust to the machine;
at first it was really a challenge to try and get the program started; then
when it did start sometiaes it would stop in the Biddle of the lesson and
refuse to continue. Having wasted that tiae it 'as aore discouraging to start
all over again. The aachine is not perfect nor aa ; but when the probleas are
solved it is exciting to communicate with a aach: >e. The aachine is ideal in
that it applies to individual needs; if I know the s ject Batter well it takes
out little tiae to finish. The mistakes I Bake ar*j carefully explained to ae

P-

3-Vl

308

and I an quizzed to see if I have understood. Although it doesn't replace the
teacher it is helpful in doing the unpleasant tasks of the teacher.

During the past 18 souths two surveys of student reaction have been completed. The first
one, begun in spring 1971, included ay personal observation log of student interaction vith the
coaputer, a collection of student paragraphs evaluating the coaputer, and a questionnaire which
is included in the appendix. None of the students were in ay classes. The priaary focus of
analysis on the questionnaire was on noticeably large percentages and apparent patterns of
response. Initially, student answers were conpiled and processed according to the percentage
response on each question. A further breakdown was printed out on the basis of the grade the
student expected in the course. Finally, two charts were conpiled based on the answer to
question no. 2. "Were you in a college prep progran while in high school?" The analysis was aade
for each of three categories.

Hes.ul.ts of the Questionnaire

The grade expectation was higher outside English B (80 percent expected an A or B).

Only five percent of these students expected to fail whatever course they were taking. Of
these five percent, all said they would like to use the coaputer again sone tine (no. 31). Sone
responses were a surprise. For exanple, 76 percent said questions are not presented too slowly.
I had been very concerned that sone exercises were too difficult, forgetting that the student
could sit at the coaputer until he was ready to answer. The sane percentage (62 percent) who
said boring material could be interesting when presented by coaputer (no. 18) said interesting
material was not boring on the coaputer (no. 22).

Sone answers were disappointing. Students were obviously nixed in their preference for CAI
over classrooa instruction. Twenty-six percent reported they could learn nore in the classroon.

English B students, as conpared with others, do not seen to think the exercises take too
long (70 percent said "No") ; 76 percent do not think the coaputer nakes the course nore
difficult. More English students said the prograns relate to their class work (64 percent) as
conpared with those working on prograas other than English (67 percent).

In the "No" colunn were several indirectly, as well as directly, positive responses froa
those Kho had not been college bound in high school. I decided to find the exact source of this
support based on grades the students expected. My assuaption was that the support nay cone froa
those who do not consider theaselves above average students. It so, reaedial prograas could be
the answer for those students on English who are striving for nininua levels of performance. The
coaputer night just possibly be teaching . these students.

Students who said they expected C or less in this course felt pushed by the coaputer (64
percent vs. 25 percent) and a greater need to talk about the prograas when they returned to
class (70 percent vs. 53 percent). In addition, they seemed nore interested in the material (no.
16 - 69 percent vs. 69 percent). Finally, not one student in this group said that the course was
a waste of tine (no. 30) or that CAI in this course is poorly used (no. 24).

Several significant figures also appear in the columns for above average students (those
who expected an A or B in the course), but they are not as impressive. For example, 67 percent
said they would like to use the coaputer again. However, nore of these students said CAI is de-
personalized instruction (61 percent vs. 45 percent) and that the purpose of sone prograas was
not clear (12 percent vs. 1 percent). The aost glaring difference of opinion is apparent in
questions 26 and 27. Only 12 percent of the better students thought that prograa errors detract
significantly, as conpared with 56 percent of the other group. However, the strongest criticisa
caae froa this group, too. Seventy-four percent said they prefer the classrooa to CAI (conpared
vith 10 percent) •

1. The total response collected (114 students).

2. The total response of students outside the area of English who were working on

the coaputer (48 students).

The total response of students working on English programs (66 students). Many
students did not respond, either because they were absent when the
questionnaires were distributed; or they failed to return then.

309

gfliigmaigfl

Hone exists for the present. One major problem for these students in responding is that
they have had no other programs to compare with those in English. In spite of all the obvious
barriers to their evaluation, the students sees such lore positive in their response to CAI than
I anticipated. In any case, the target is the remedial student, and he appears to want help,
regardless of the aaount CAI aay provide. In fact, it aay be that the less securo a student is
about his ability, the eore he eay need a continual tally and e/aluation such as is possible
with CAI.

lie V§ las of CAI

Insofar as the value of the computer, I cannot coaaent whatsoever about cost effectiveness,
perhaps the lost important question for you. On our caapus, the computer was there beiore CAI.
To the question of whether CAI in English provides a valuable learning experience, the answer is
both "yes" and "no." "No" because many students in remedial English are poorly motivated; many
prefer sitting in a passive classroom situation; this is not possible with a computer. They

cannot skip work by skipping class because the computer waits until they find tine to work on

it. Consequently, CAI is a burden and a responsibility; it also renoves the contorting kind of
contact with the instructor to the extent the student spends nuch of his tine with an exacting
type of neasure of what he is doing. I would say '•yes*4 to it as a valuable learning experience
because it enables instructors to write prograns tailored to unigue student problens, even
though the prograns are linited by their ability to design then. I would say "yes” to it because
the conputer allows a kind of remediation wherein the student is not able to perforn at a
certain level. In nost of the prograns, for exanple, the first question is the nost difficult

rather than the nost sinple. If a student is not successful in the nore difficult tasks, he is

directed to a lower level of difficulty and later back to the nore difficult questions. The
answer is "yes'* also because it rewards the nore attentive student. Students are not io a
classroon for fifty ninutes, but at the terninal for however long they need to be. Purthernore,
the conputer shifts the responsibility of the course fron the teacher to the student. He is no
longer ible to present the usual student conplaints about not having heard the assig nnent. • • not
having been there for the lecture. At the end of each program is his writing assignaent,
primarily to have it in writing, and so that he does not begin writing until he has gone through
the theory involved in his particular assignaent.

In an ideal systen, the computer would understand English, of course. In addition, it would

have;

I. A terminal which is quieter than a typewriter.

J* A maximum response time on all scanning routines of three seconds.

J. Extendah1'' workspaces.

4. Specially designed type balls which would permit upper and lower ca:-e letters.

5. Sufficient storage capacity to accumulate and evaluate statistics related to
student responses.

h. Some means of alleviating the monotony of program display. The student should
be able to easily distinguish introductions, examples, specific instructions,
and text. ?ossible answers to this problem night be varying the typography or
presenting some information with audio cassettes.

7. Programming aids for language analysis* the ability to analyze a paragraph for
syntax, grammar, and vocabulary. What such a systen would require basically is
much greater storage capacity and special routines, enabling one to define
grammatical rules and lexical categories that could he interpreted to analyze
sentence structure. The manipulating capability is already available in various
compilers and compiler approaches developed tor scientific application. The
ideal learning situation would be odo in which the student would not be
assigned work in remedial English at all. He would be assigned to a regular
freshman composition course. When he had problems, he would be assigned to
specific computer programs designed to help him overcome them.

Program design in CAI presents a paradox. The programmer knows more about the limitations
and potentials of the system, yet those programs most useful in English were designed by the
instructor. Perhaps the programs are more germane when written by an instructor who knows little
of the programming language than by a programmer who is unaware of oh actives or instructional
techniques. The programmer works for the system; the instruct' designs his course for the
student. "Science,*4 in the form of a computer, may provide the answers, but "art,” in the guise
't the instructor, must still ask the right questions.

313

DPI LLI EG SPAHISH f EBB FORES OH REEOTE TEREI H ALS

Robert Phillips
Hiaai University
Oxford, Ohio 45056

Telephone: (5b/ 529-2733

Introduction

Two years ago, the Computer Center of fliaai University added the tiae-sharing reaote
terainc language APL to its systea, and a aeaber of the staff suggested to ae that I learn the
language and develop soaething of pedagogical value for Spanish, students. After soae thought, I
decided that there vas a need for Spanish students to drill verb foras.

The verb is the heart of the sentence, and Spanish verbs have rather coaplicated aorphology
as compared to English verbs. A typical Spanish verb has about forty-two different foras,
considering all tenses and aoods. Because of this plethora of foras, soae students have
difficulty mastering thea. And, if they cannot handle the verbs, they juct cannot produce
accurate sentences, either orally or written. Soae of our students coae from an aud io- lingua 1
background, in which aost of their learning of verbs has been done orally; a few of these have
never learned to write the vt'tbs accurately. Others have difficulty learning the verb foras by
repeating then in tuO language laboratory; they need soae type of drill which they can do in a
written aatner. Still other students need wore practice than that afforded by the exercises in
their book or on the tapes in the language laboratory. And, soae few students are frustrated by
the speed of the tapes or the teacher, saying that they could get the verb fora right if only
the teacher or the tape would give then enough tiae.

Desiderata in Drill Progra as

Bet">r* starting to write a program to provide the students with drill, I felt that there
were five points which were necessary if it were to be successful:

1. JJ^ndoaness. The drill iteas had to be presented to the student in random order, so

had to go through coaplicated coaputsr ritual to use the drill, he might be turned
off by it, considering it to be lore trouble than it was worth.

One thing at a tiae. If the student were having trouble with regular past-tense
foras7~he would not be helpea by being given irregular foras. Therefore, each drill
should concentrate on one at a tiae.

Ease of for teacher. Proa the beginning, I felt that the drill iteas would ha7e
to~be changed as the students aeguire new vocabulary and different complications in
the verbs. To make this possible, it has to be easy for soaeone to make the changes.

The "Easy” Drill Package

With these five desiderata in aind, I wrote the program for a verb drill for the students.
The tiae-sharing reaote- terainal concept seeied right, because the student could work at his own
pace, free froa the tensions of tiae present in the classroom and the language laboratory.
Furthermore, the remote terainal is very auch like a typewriter keyboard, and virtually all
students can use a typewriter, even if it is only on a "hunt and peck" scale. And, it is alaost
completely free of the paraphenalia of other computer applications: no job cards, no compiler
parameters, no data description cards, etc. Once a progra i is developed and debugged, all the
student n'ed do is sign on, invoke the prograa, and then get to work on it.

I should add parenthetically here that I was greatly influenced in the design of ay
programs by a packaged part of the APL software. There is a mathematical drill called EAS7DRILL
giving the student practice in using APL*s aa theaatica 1 operators. As part of ay learning of
APL, I had used EASTDRILL a*id had liked several features of it. Therefore, soae of the specifics
of my drill procjraa were copied froa EASTDRILL.

tha t~he~would not learn the correct response in relation to the item preceding the
one he was working on.

2. feedback. The student must be told immediately if his answer is right or

wrong. Often, a~studentfs problem is that he writes the wrong answer while doing his
homework and does not find out tor a day or two that it was wrong.

3. Ease of use fot student. If the student had to learn anything about programming, or

31 I

I developed a package which I call BAST and which the student invokes by typing 'BAST.1
(The student who needs remedial help usually wants something that is "easy." Since there is
another package called HARD, which is discussed below, the student is assured that he is indeed
getting the easy drill.) This progras has nineteen different drills in It (each drill is on one
"tense"), and the student chooses one at a tine to work on. He can, whenever he wishes, change
to any of the others. Each of the drills has twenty-five stimuli. There is also a "hint"
associated uith each of the stimuli. The student can ask for the hint at any tine, or he can ask
for the correct answer. If he does not kttJw the answer, it nay be better for him to get it,
rather than waste tine entering wrong answers, which he nay accidentally renenber.

When the student chooses the drill he wants to work with, he is given directions on what to
do, and then a stinulus is presented to hn. If the answer he types is correct, he is told that
it is correct, and another stinulus is presented. If his answer is incorrect, he is told so and
asked to try again. If his second response is correct, another stinulus is presented. If the
second response is incorrect, he is told that he was wrong, the correct answer is typed for hin,
and the hint associated with that fora is given.

One problen which occurred early in the developnental stage was the randonness of the
stinuli. I had progranned it to give the stinuli in randon order. However, I found that the
student got annoyed when it repeated stinuli which they had already gotten correct several
tines. Therefore, I modified the progran. How .it has in its nenory a chart with twenty-five
zeroes, one corresponding to each of the stinuli. H hen tUe student get^ the answer correct on
the first try, the zero for that stinulus is chai ged to a one. That stinulus will not be given
to the student again until all of the zeroes have become ones. (Vhen that happens, all of the
ones change back to zeroes.) The student does not know that this is happening; he only knows
that the "problen" forns cone back again and again until he gets then right. There is one
strange phenonenon that occurs, although I did not progran it. The students believe that if they
miss a certain forn, that forn is repeated after two or three intervening stinuli. Indeed, nore
than one student has told ne that he "knows" that I wrote the progran so that it would do that.
It is apparently due to the fact that he rapidly disposes of the "easier" forns, and the progran
has to return to the forns which ho has missed.

At any tine during the drill session, the student can change to another drill or stop the
drilling. Since there is nothing sequential about the drills, he does not interfere with any
pedagogical sequence by changing when he wants. If he does want to change, he nerely types
’CHANGE.' It types out the score he got on the drill he was doing, and then repeats the list of
available drills. He then chooses the new drill he wants to work on.

It is quite ea3y for the teacher to change the stinuli and the answers for any drill. It
requires typing in the twenty-five stinuli and the twenty-five answers, and the hint number
associated with each stinulrs. After each list is typed, the entire list is typed back so that
the teacher can check it for correctness and nake corrections where necessary. If the teacher
wants, he can have it type out the entire drill: directions, stinuli, answers, and hints.

What the Student Does

This drill is very easy for the student to use. Let ne describe briefly what he has to do.
First, he signs on by typing an eight-digit nunber. The computer responds with a welconing
nessacre. Then he types ' ) LOAD 1 EAST? AH,' which tells the systen to load that particular package
into its nenory. Then he types 'DRILL,' which starts the drill program. It types a welcome to
the Spanish verb drill and asks if he needs conplete instructions.

If the student answers jes (by typing 'TBS' and pressing the RETURN key), it types brief
instructions, which sunnarize infornation that he has already read on a hand-out infornation
sheet. It tells bin to use accent narks and how to show then. (That was a problen: APL does not
have accent narks. However* letters can be underscored, so we have an underscored letter r;tand
for an accented letter.) If he nakes a typing error, he is told to type an asterisk, press the
RETURN key, and start typing the word over. It tells hin to type 'PLEASE' if he wants a hint, or
'HELP* if he wants to see the correct answer. It reninds him to type 'STOP' or 'CHANGE* if he
wants to stop drilling or to change to a different drill.

After the brief instructions, which take 1.3 minutes, a conplete list of the nineteen
drills is typed, and the student is told to enter the nunber of the one he has selected. After
he presses the RETURN key, the directions for that drill are given. For one drill, the
instructions say that a subject and an infinitive will be given; he is to tvpe in the present
indicative forn corresponding to that subject. For another, it says that a verb will be given in
the present tense, and he is to give it in the preterite forn (one of the two simple past
indicative tenses) , keeping the sane subject, etc.

After the stinulus is typed, the student types his answer, and gets a response fron the
conputer. It is either "CORRECT" or "WRONG - PLEASE TRT AGAIN." If it was correct, another

312

stimulus is typed and he continues. If it vas wrong, he tries again. If he sisses the second
tine, it types "STILL HROHG “THE C08KBCT ANSWER IS", the correct answer, and the hint to help
explain it.

It goes on for as long as the student wants to continue with that drill. Tte important
thing is that the student can continue working at his own pace for as long as he wants. If he
wants to spend three hours on one drill, he nay do so, providing terninal tine is available.
When the student types 1 STOP* or 'CHANGE, 1 it types out his score, giving bin the nunber of
stinuli he attenpted, the nunber right on the first try, the nunber right on the second try, and
the ounber he failed. It disregards those for which he asked for help.

Pron the student's point of view, then, this is very sinple to use. He has to be able to
type the forns correctly, but if he does nake a typographical error, he can correct it sinply.
The student does not have to understand anything at all about the way in which the prograa is
worked. He is the sole judge of when he has drilled enough, and he works at bis own speed.

The student does not realise it, but at the tine that he is drilling on one particular
tense, he nay be getting passive drill in another tense. In all of the drills but three, the
stinulus is another verb forn, generally the present tense. He Spanish teachers find that the
students often look at a verb forn and do not pay any attention to what the subject of the verb
is. This is due to a difference between English and Spanish: English nust have an explicit
subject, while in Spanish the ending of the verb tells what the subject is. Thus, when drilling
the future tense, the student nust correctly identify the subject of the present- tense stinulus.
He nay, for exanple, look at the present-tense verb, assune that the subject is "I9* and type the
future fore accordingly. When ho gets it wrong because the subject was supposed to be "he," the
student is forced to take another look at the stinulus and to identify the subject correctly.

The "Ha£d" Drill Package

I had sone students in nore advanced Spanish classes who tried the drill package described
above, but who found that it vas too easy and too restricted in what it offered. They wanted
sonething which would present then with various tenses and a greater variety of problens than
EASY has. I decided that to be worthwhile, a nore conplex drill would have to give the students
drill with at least forty different verbs, in nost of the tenses, and with all subjects. Such a
drill would involve a total of 2,800 different forns, and I was not about ready to type in 2,800
stinuli and 2,000 answers. Furthecnore, there is not enough nenory storage available in APL for
that a&ny words. I wondered if it would be possible, instead, to give the conputer stens and
endings, and then progran it to generate the forns.

This intriguing problen vas one which the innate progranner in ne innediately had to solve.
I did write a drill which does specifically that. It has in it fifty different verbs of every
type: the conpletely regular ones, those which are slightly irregular, those which are very
irregular, those whose sten changes forn, and those which have to change spelling when certain
endings are added. This progran stores the stens of the verbs and all possible endings. It has
sone very conplicated tables which tell it vbat sten to use for each particular subject in each
particular tense, and what ending to use for that subject in that tense. Thus, each tine the
progran calls for a verb forn, the progran itself generates the forn: no conplete forns are
stored anywhere. In ny final design, there are fifty verbs, nine tenses, and eight subjects for
a possible total of 3,600 forns.

For the stinulus, the terninal types out an infinitive, a subject, and the nane of a tense.
The student is then expected to type in the correct verb forn. The actual answer is not given by
the conputer unless the student nisses it in bis two tries. The student does not see the
conputer generating each of the forns fron the stens, endings, and tables, but this process is
done twice each tine through: once to generate the infinitive (go conplete forns are stored) and
once to generate the correct answer.

Before the progran could be written, it vas necessary to arrive at sone type of analysis of
Spanish verb norphology. Although I quite fimly believe that Spanish verbs consist of three
"slots11 (the first being the "sten," the second being the "then vowel," and the third being the
"person-nunber (subject) indicator"), I decided, for practical progranning purposes, to divide
the verb into two parts: sten and ending. One reason for this is that a "three-slot" analysis
has to nake use of a nunber of "zero" allonorphs. That is, the slot is enpty in that particular
forn. If one were to use the enpty slots, the progran would have to look for enpty slots and
then ignore then. Although quite possible to do, it would nake the prograa nore cluasy. Since
the purpose vas to generate verb forns rapidly - and not to give lessons in the theory of Spanish
verb norphology— I decided that it would be better to have an "elegant" progran based on a nore
"rough and ready" analysis of verb norphology.

Another problen vas what to do with the perfect tenses, since they also had to be drilled.
The perfect tenses consist of a forn of the auxiliary verb haber plus the past participle. The

313

past participle can be forned as a s t e ■ and an ending (although with difficulty in the case of
irregular verbs) , but then one would also have to take a s^ea and an end.ing foe the auxiliary
haber, which has to show tense and subject. I solved this problei by calling the entire past
participle the stei and the auxiliary verb (in its complete foras) the ending, and then putting
the "ending" in front of the stea, with a space separating the two. Certainly an inelegant
solution froa the point of view of Spanish verb norphology, but one which fitted the needs of
the situation guite well.

For students working at the aore advanced level, I felt that working with only one tense at
a tiae was unnecessarily restrictive. However, it would not be right to force the student, to
work with all nine tenses if he wanted drill in only one or two. Therefore, the program was
written to allow the student to work with whatever tenses he wants* If he wants to drill only
one tense, he can do so. Or, he can work with two, three, four, on op to all nine. Part of t h a
"prel ini na r ies M consists of having the student select the tense(s) he wants to drill. Froa then
on, he works only with those tenses. Thus, he can drill one troublesone tense, review a group of
tenses, or review all of the tenses at one tine* The one thing that is not possible for hia to
do is to select a certain type of verb (such as irregular futures, irregular preterites, etc.)
to work with. He has to take all types of verbs with the tenses he has chosen. This, however, is
apparently not felt to be a lack by the students, for none has ever asked ne if it would be
possible to sub-divide the verbs by class.

This prograa, which is called HARO, is nodeled on the EASY prograa described above. It was
not possible to have a list of hints. The prograaaing of hints would be so exceedingly coaplex
(it would involve a t hree-diaensional table of nuabers which would be fifty by nine by eight)
that £ decided to forego the hints.

The package has the advantage of never needing any changes by the teacher. Since there is a
total of 3,600 different coabinations of verbs, subjects, and tenses, the student can drill tor
a very long tiae without feeling that he has exhausted the possibilities of the drill.

Froa the student's point of view, this prograa works very nuch like the EAST drill outlined
above. It gives hia siaple general directions, then types out the nine available tenses (present
indicative, iaperfect indicative, preterite, future, conditional, present subjunctive, past
subjunctive (-r* for* only) , present perfect indicative, and past perfect indicative). He types
in the nunber^s) corresponding to the tense (s) he wishes to drill. Froa then on, the stiauli
consist of an infinitive, a subject, and a tense. The student has two tries to get it right; if
he does not get it right on the second try, the correct answer is given to hia, so that he can
learn it and analyze why he was in error* Although he cannot ask for a hint, he can ask for the
correct answer by typing 'HELP.'

When the student wishes to stop, he types 'STOP*' As in the EASY drill, it types out the
number he atteapted, the nuaber right on the first try, the nuaber right on the second try, and
the nuaber failed. In addition, it breaks these data down by tense, showing hia how aany he
atteapted of each tense, how aany of those were right on the first try, etc. In this way, the
student can see where he is having probleas, and concentrate on those areas the next tiae he
drills.

Operating Considerations

Although the terainals are easy to use, and APL is not complicated, there were a few
difficulties which annoyed the students, and which had to be overcone if the drills were to have
maxinun pedagogical value. The first was the natter of typographical errors. To correct an error
in APL, you aust backspace to where you aade the error- and it's hard to see exactly where that
was with the I8H t ype-ball - and press the ATTENTION key. Then you resuae typing froa that point.
Students get confused by how far back to backspace, and don't know what to do if they go back
too far. So, t progranned a rather easy way to do it: the student types an asterisk, presses
the RETURN key, and starts the answer all over. They find this considerably less conplicated.

Another problem which occurred was with the terainal itself. Our terainals have plastic-
type-shields which cover the first couple of lines on the paper. While one can see through these
shields, they are not easy to read through and they annoyed the students. Therefore, when it
types the stinulus, it advances the paper two extra lines, so that the stinulus is above the
type-shield. The student can see it easily.

Perhaps the gravest difficulty was with the randonizing of the stiauli* While the APL
systea has a very fast, very easy randon-nunber generator, it has one grave fault: it uses the
sane seed each tiae the workspace is loaded. You can picture the generator as being an
inf i nitely-long string of nuabers which is always the saae. That aeans that you get the sane
randoa numbers in the sane sequence each tine you use it: that is not randoal If the students
were to use different tenses each tiae they used the drill, there would be no repetition
noticeable to then. However, I had a

5 . i %

couple of students who always used HARD drill to drill all

nine tenses. They discovered that each tine they used the progran, the sane subjects, verbs, and
tenses case up together in the sane order. Clearly, if they vere to get the full benefit of the
drill, I had to Bake it so that the randoa nuabers vere indeed randoa, rather than predictable.
This I did by having the progran get the tine of day in Billiseconds fron the central processor,
convert that into hours, ainutes, seconds, and Billiseconds, and then use those nuabers in a
loop vhich asks the generator for randon nuabers. This loop gets a randoa nunber of nuabers froa
the generator, but does not print then out; sonetiaes it vill ask for only five or ten, it nay
ask for over a thousand. Thus, running the progran through this loop in effect starts the drill
at a different place in the string of nuabers each tine it is used. Again, the student is not
avare that this is taking place- the processor is doing it vhile the terninal is typing out the
instructions. Both BAST and HARD have this randoaizing routine.

Resuits

What has been the student reaction to these drilling prograas? First, ve have guite linited
terninal tine. (There are only eight terninals in the university, and they are available only
three hours per day, giving only twenty-four terainal hours a day, five days a week.) Students
are linited to thirty-minute periods on the terninals, neaning that only forty-eight students
can use then each day. Our Spanish students have to conpete for tine with students in Systens
Analysis, Nath, Physics, Business, Psychology, Sociology, Cheaistry, Political Science, and
Education Psychology. Purtheraore, the systea is available only froa 4:00 pa to 7:00, vhich
covers the dinner hour. Because of these Uniting factors, ve nade announceaents in classes that
the drills are available, but no student vas obligated to attend. Nonetheless, the students vho
elected to use this systea have been quite enthusiastic about it. During the first quarter of
71-72 acadeaic year, ve logged approxiaa tely forty hours of terainal tine by Spanish students,
vhich aeans approximately eighty different uses by students. Very fev first-year students vere
using it, because they had had only the present tense during nost of the quarter. Our prediction
is that it vill be aore videly used by then during the second quarter, vhen they have to learn
five aore tenses.

During the vinter quarter of the 70-71 acadeaic year, ve vere able to reserve tvelve
"slots" per veek, and usually had eleven students sign up for those tines. These vere all first-
year students, studying those tenses. The HARD drill vas no 'c then available for the advanced
students.

All in all, I feel that our students are aaking good use of the terninals. If ve had
greater availability of terninals and terainal tiae, ve vould have aore use. Hovever, if too
aany aore students vant to use the terninals nov, ve siaply vill not be able to accoaaodate thea
vith the resources at hand.

In use, the students seea to enjoy doing the drills, not finding thea to be so boring as
they profess to find the oral drills in the language laboratory. Many of the students say that
it is "fun" to vork on the terainals. Batching vits vith the coaputer. None seen to be bothered
by having to type their responses. Hy experience has been that the students are aved by the
mechanical aspects of it for about the first five minutes (the terainals type at fifteen
characters per second, vhich is adaittedly avesoae) , and feel slightly uncoaf orta ble during that
time. After the first five ainutes, hovever, they adjust very veil to the situation. We find a
very high percentage of students vho cone back for aore drill.

Hov much can a student do in the thirty ainutes allotted to hia? It varies greatly froa
student to student. Those vho are very slow vill do about Iventy-five stinuli. This aeans that
in the EASY drill, they von*t even cover all of the stiiuli one tine through, unless they get
them all right on the first try. Nore coaaon is about forty stiauli. Last year, one girl
regularly did betveen ninety and one hundred stiauli on the HARD drill. But she alaost never
made a mistake and could type fast, besides. Host students do not feel that thirty ainutes at
one sitting is quite enough. I suspect— but have no vay of knoving - that over an hour vould lead
to a situation of diminishing returns.

Do the students learn froa this? Hy ansver is definitely yes, but I do not have concrete
data to prove it. Because of the limitations, it has not been possible to do formal experiments,
using control groups, etc. In the very early stage of development I used one of ay first-year
students as an experimental subject. I had given his class a quiz on a certain tense, and he had
missed nine out of tventy-five items. He then drilled on that tense for over an hour on a Priday
evening. On Monday, I gave another quiz on the sane tense, and he aissed only tvo out of tventy-
five. Pever than half of the foras on the quiz vere included in the drill: he had learned the
process of formation, and not just memorized certain foras.

In my third-year coaposition class there is no reviev of verb foras. I siaply tell the
students that I assume they knov all of the verb foras. After the firsL coaposition of the
quarter- on vhich there vere nuaerous verb-fora errors I announced the availability of the HARD
drill and told thea vhere to get the inforaation sheets. Again, no statistics (ve do not keep

318

n C

records in our Departaent, since we do not bare a terainal) , but the nuaber of verb-fora errors
on coapositions has greatly diainished. Doubtlessly, aany of the errors on the first
coapositlon were due to the students1 having been away fro* Spanish during the suaaer.
Nonetheless, enough students have told ae how helpful they have found the drills to Bake ae
certain that coaouter-assisted drill in Spanish verb foras has a valuable place in our
university.

What is the future for this type of drill? X believe that it is definitely here to stay as
a valuable adjunct to classrooa instruction. I weald like to see the drills expanded to cover
other foreign languages as well. 1 believe, too, that the concept of the drills can be extended
to iteas other than verb foras. While I do not envision the possibility of having the coaputer
check a student’s translation froa English into Spanish, it could be used with certain selected
topics, such as the use of ser versus estar. the use of the preterite versus the iaperfect, and,
perhaps, even the use of the subjunctive in coaplete sentences. Naturally, each type of drill
will require a considerable aaount of thought on the pedagogical goals, and then on how to
achieve those goals in a prograa.

Our greatest need now is for aore facilities, so that the reaote-terainal tiae-sharing
systea can be on-line at all tiaes. As it now stands, our language laboratory is a valuable
help to the students. I would like to see one terainal on-line at all tiaes in the language
laboratory. Thus, the students could coae to drill in the language laboratory in various ways:
orally for those things aost appropriate for oral drill, and on the tecainals for those iteas
which can be profitably drilled and reinforced by writing and repetition.

The author expresses gratitude to B. Arthur Fiser, Director, and to David Probert,
Consultant, both of Acadeaic Coaputer Services of Sinai University, for their constant
encouragenent and help, and for their unflagging dedication to the principle that the coaputer
should help all segaents of the university coaaunity, including foreign languages.

The Future

ACKNOWLEDGEMENTS

ERIC

316

' • •*.

COMPUTER-AIDED GRAPHICS AS AN ART FORM FOR THE ARTIST

Grace C- Hertlein
Chico State College
Chico, California 95926

Although course development for the teaching of Computer Art for Artists began at Chico
State College in April of 1970, actual teaching of the course did not begin until September,
1971. The course was offered ;n the fall of 1970, tailored to the needs and interests of
artists* yet it failed to reach minimum enrollment. Other institutions have invited artists to
experiment with computer-aided creation and have experienced the same hesitancy on the part of
the artist to use advanced technology to create wcrks of art. A review of the literature
regarding art and technology, and perusals of avant-garde technological exhibits reveals heavy
use of industrial mat rials and procedures of fabrication, yet a low level of complex machine-
aided creation. Thus computer-aided creation represents t.he apogee, at this moment, of complex
machine-aided creation. When viewed from this attitude, it is not surprising that the artists
are reluctant to leave the known manual world in which they have confident capacities.

At first this appeared ironic to the instructor, an artist ''converted" from the ranks of
fine art, one who understood clearly the difficulties that the humanist experiences when
confronted with the complex and demanding computer.

Our course description for artists is as follows:

1. Investigation and use of computer graphics as an art form for the n on- programmer
(artist) ;

2. Use of computer graphics languages combined with art techniques familiar to the
artist, applicable to the creation of computer art graphics;

J. Development of design planning, execution of computer graphics leading to a personal
style in computer art;

<4. Applications to painting, sculpture, weaving, printmaking and applied design.

Prominent writers, including Holland, Milic* and Mesthene, have detailed tne problems that
the humanist faces in his first confrontation with the computer. The instructor in this course,
an artist- teacher, with long experience in fine art and in the Leaching of art, had experienced
first-hand the psychological difficulties that the artist encounters witnin initial computer-
aided experimentation.

The plan was to take the known world of art, creativity, material usage, design
proficiency, and bring it to the unknown world of the computer. In this manner, one proceeded
from the known to the unknown.

Course objectives are:

To develop an acceptance of
computer-aided creation;

com pu ter

graphics as an art

form by an exposure

To afford in-depth experiments

tion of

machine capabilities.

relating to known

art

techniques and unknown computer
creation of computer art;

techniq

ues, affording early

proficiency in

the

J. In-depth study and use of art materials, design techniques, using simple programming
as the basis for experimentation.

It appeared during our first year that the artists were unwilling to "jump the crevasse" ot
the unknown, even with a sympathetic and qualified guide.

Interest on the part of Computer Science s
generous listing of science students awaited entry o
ot 1971, a group of seven artists signed up for the
large number ot Computer Science students applied
accommodate both groups, on an experimental basis
our evening course, with the provision that each gro
extra tutoring for the artists by more experienced
more sophisticated programming than the artists woul
group.

tudents in computer art was very
n an additional reserve list. I
course. This presented a proble
for the same time slot. I
, we put artists and programmers
up would help the other. This
programmers, and a taster intro
d have encountered in an isol

high, and a
n the fall
o, in that a
n order to
together in
also meant
duction into
ated artist

317

320

Originally we had planned to use an industrial drafting program for the artists. This
language is easier to comprehend,, and there are built-in software capacities, such as rotation,
mirroring, etc. tnat afford moderately sophisticated art graphics within a lew weeks. The
instructor had used this system in early research, and had also made use of this easier language
in tne first pilot group of programmers. At that time, experimentation with the first
programming group revealed a larger variety of more artistic and varied graphics when using this
system. It also revealed, when contrasted with Fortran, that the highly advanced programmers
scorned such an '’easy" language and disdained its usage as beneath their technical capacities!

However, witn installation of a new computer system, the drafting system compiler proved
excessively inefficient time-wise, and the decision was made to use Fortran with the new group
or artists, using tutoriil help f rora programmers.

There are many institutions desirous of teaching such a course, and many await the "ideal"
system, the "ideal" language. In the midst of economic realities, the colleges and universities
find that it they wisn to pioneer, they must make do with what they have, and just begin.

This is what we did. We were cognizant of the advantages and disadvantages of such a
procedure, but felt that more was to be gained than lost.

The question then might De, what is the ideal artist system?

I. A digitized sketchpad or digitizer;

A. CR1 lightpen and/or joystick input;

J. dasy prog la mm ing Languages designed for non- programmers.

Josignors, artists, humanists, all cry for an easier mode of input. Tney do not wish to
learn a second career. Ye t cognizant of this need, the above "ideal" system has disadvantages:

1. The artist often transfers his manual art to the machine and fails to explore the
innate nature of the material or media, in this case, the computer. He then fails to
discover the uniqueness of the media. This "truth of the material'* is more readily
discerned via sophisticated programming and mathematics.

A. The artist repeats things on the computer that might better be accomplished manually,
and the resultant output resembles a bastardization of manual art, via the computer!

d. The artist fails to appreciate the uniqueness of the computer, and to perceive the
wedding of art and technology, which is a union of science and art.

Thus, easier modes of input result in easier output of initial graphics, but at a lower
level of technical proficiency- Interdisciplinary means the union of two disciplines, i.e., the
practitioner learns two disciplines, and combines them into a balanced whole. And in computer
art, after the initial exposure, we are always aware of the level at which the computer is being

used .

Our small group of artists were isolated oace a week for two hours with an assistant in a
laboratory session. They started from scratch:

1. What is a computer? How does it work? What can it do?

2. What is a program? How does one write a program in FORTRAN.?

3. They learned to keypunch, and to debug their own programs.

4. They used very simple practice exercises to gain proficiency in programming, to gain
accuracy, and to develop confidence in their new capacities.

During the other three hours a week, they met with the programmers for lectures, films,
laboratory programming and sketching sessions. Our mixed group of artists and programmers fared
fairly well in many ways. Informal in-depth discussions between artists and programmers

regarding difficulties helped both groups to adjust to new interdisciplinary creation. Problems
encountered were:

1 . og^a mm l njq Difficult ies. The artists were not mathematically oriented, and even

with help from programmers, they experienced difficulty in using FORTRAN. We used
point to point programming at first, then advanced to more symbolic input. We played
substitution games, so that symbology was merely using something for a known
something else. Programming then became game- like and more enjoyable.

318

Im Thinking Machine in Desi g ping Compose n fs. Both groups had difficulty in designing
tor the computer. Laboratory sessions, L^ackboard illustrations by the instructor,
and sketching sessions clarified this concept. The reiterative capacities of the
computer were exploited, and regular progressions of increment or decrement were an
inteyral part of designing. The "esthetic" ot the computer became a goal in
designing and programming.

Interdisciplinary Wea knes ses. Both overcame their initial feeling ot inadequacy.
Fach group was encouraged to base their new work on their dominant strength, and to
progressively yrow in the new discipline.

4, Verbalization ol Ideas. Programmers and artists alike experienced difficulties in

written and oral verbalization. While programmers had difficulties in initially
analyzing subjective and objective ideas,, their scientific training afforded taster
growth in sucn analysis. Artists, on the other hand, througn "mental programming"
nad relied upon intuitive, emotive, non-ana 1 ytical methods to create, and their
verbalization and analysis was more difficult than that of programmers.

In addition to those difficulties, our beginning classes were all running preplanned mode,
although advanced classes had the option of "hands-on" running. It is the writer’s stLong
opinion, that it at all humanly possible, computer art should be run in the "hands-on" mode:

1. Students require the emotional involvement ot seeing ink applications develop on

varied art papers;

2. They need to see for themselves where the design may be overdeveloped;

j, Myriad ideas for development are perceived when the artist runs his own graphics, as

natural variations from first creation. The whole purpose is to "see" as you are
working, and not merely to i n te llect ua li ze theories.

To compensate for this preplanned mode, we introduced randomization earlier to this mixed
group, including the artists. We also used known, tested "design states" tor varying graphics,
using examples ot s t uden t- teac her work, slides, blackboard illustrations and group brain-
storming sessions. With these methods, students were able tc vary their components and achieve
more sophisticated graphics than they would have, had they "discovered" such states in "hands-
on" running ot their work.

Treat emphasis was made of the concept of recognition ot known parameters, whether they
were equipment, languages, or one’s own limitations. The ideal world is never ours, yet
increasingly, by cognition of where the limit occurs, one may affirmatively create within these
limits. To tnis beginning group of mixed students, preplanned mode was a limitation, yet we
introduced more advanced concepts to compensate tor such a seeming hindrance. Within the next
semester, these same students will focus on "hands-on" running modes, participation programming
and running states, painting techniques, all of which are not possible in preplanned modes. Yot
by contrast, these same students examined graphics that were preplanned, randomized, painted,
block-printed. Handomized graphics, with stated limits, often emerged as their preference,
revealing a more "natural" variation of* the subject than regular preplanned, participant
programming or painting techniques. In other words, every mode of programming and running,
every system has advantages and disadvantages.

In summary, cognizant of the advantages and disadvantages under whicn this group operated,
artists learned more technically about the computer:

1. The artists learned the mechanics ot programming, keypunching, debugging, editing

pr og rams.

2. They experienced new insights into contemporary art, and more, that of complex

machine-aided creation, by doing, and not just reading a^jut it.

1. They learned to program fairly well in FORTRAN# and to symbolically perceive

mathematical relationships that were moderately advanced tor such a group.

4. They perceived a dimension of logical thinking, which they began to apply to other
areas. Some felt tnis alone was worth the travail they had experienced.

b. Programmers developed multi-purpose (more complex) subroutines for artist use, and

the artists learned to understand more complex programming in this manner.

Frustration was overcome gradually. Students felt a great sense ot achievement in
their esthetic and intellectual accomplishments.

7. Affirmation of technology per se, as a part and parcel of our society resulted fro*
this exposure.

H. Student artists learned to appreciate more fully the ability to analyze and define an
artistic problem, and to seek varied and alternate solutions to such a problea. in
other words, they gained fuller control of their own creative processes.

9. The majority of the artists felt they had passed the period of difficulty, and plan
on taxing the advanced course, to continue their computer creation.

10. The artists emerged with a new intellectual independence, i.e., they had learned a
new way of thinking, which liberated them from relying totally upon intuitive
processes alone to create. They now had not only control, but more sophisticated
means of achieving creativity.

It is obvious from the loregoing that the artist experiences greater psychic difficulties
in '’going interdisciplinary" than does the programmer. The world of science is more demanding
than the world oi art. This brings up the interesting question: "Is it easier to learn to

create art via manual modes than it is to learn to use the computer in a moderately
sopnistica ted manner?" j

The answer is that it is tar easier to learn to paint in watercolors, to sculpt a head in
clay, than it is to learn the complexity of the computer.

but a far more interesting concept is this: It is moderately easy to take a non-

projrammer, a non-artist, and to teach this student how to program, and simultaneous! y how to
create, using the computer as an aid in creation. We rely on the innate~creative capacities of
the human being, merely releasing them using experimental techniques.

Thus using the computer cannot only be a complex learning situation, it may be coupled with
the teaching of art and the creative processes.

USE OF THE COMPUTER IN INTRODUCTORY ALGEBRA

Thomas Halley
The Ohio State University
Columbus, Ohio 43210
Telephone: (614) 422-5710

This is a descriotion of the use made of tne computer in an introductory algebra sequence
given at Ohio State. The algebra involved is well Known and several ot the procedures described
have neon done by ha id for many years. While a good deal of energy has been devoted to the
question ot now computers might be employed for research in algebra (see [ 1 ], [2]), there seets
to be a dirth ot information about ways machines can be employed in an undergraduate algebra
course. There appears to be great potential in this area and it is likely that interesting work
has been done here which has gone unannounced or unnoticed. We hope that this paper might
stimulate more discussion about past results and future plans.

The sequence described is three quarters work covering number theory, linear algebra and
abstract algebra. By treating this as a full year seguence rather than three separate courses
we hope to avail ourselves of opportunities to interweave the abstract with the concrete in a
natural manner. Utilization of the computer is another step in this direction.

The students involved are primarily juniors majoring in mathematics. Their career goals
after a bachelor's degree are widely varied; medicine, law, sociology, industry, and indecision.
Perhaps one fifth are interested and capable ct doing graduate work in mathematics (most
undergraduate math majors who might be expected to go on to graduate school are identified
earlier and counselled into the honors sequence) and so no pietense is made of giving a graduate
preparatory course.

The system used was CPS (conversational programming system) with an IBM 360/150. Programs
were written in the CPS PL/1 language. Communication with the machine was via IBM 2741
terminals — in appearance, a typewriter connected to the computer by telephone. For the beginner,
CPS offers some significant advantages over punched cards. As the name implies, while the
student is typing a program, he is engaged i ri a conversation with the computer. If an
instruction is incorrect, the computer replies immediately with an error message. It the
programmer wants to alter the program while it is running, he may stop execution and do so.
These and other options make it especially attractive for inexperienced individuals who are
prone to ensnare themselves in numerous programming errors.

In a venture such as this, where no previous experience with computers is required, one
serious difficulty is teaching students to program. Fortunately about halt the class had some
previous training and several were quite expert programers. Experience was advantageous, tor
essentially we adopted the attitude that programming is a skill one learns by doing. After
discussion or the basic commands and a few illustrative examples, students were given a fifteen
page handout containing a description ot the most commonly used PL/1 commands and conventions
and were then Lett on their own. From time to time common difficulties arose which were
discussed in class.

Student response at the end of the quarter indicated that this procedure left something to
be desired. Apparently more care needs to be given to the content of the instruction sheets and
more class time devoted to discussion and illustration of fundamental techniques. But no matter
when an individual begins to program, he encounters frustration. Since we intended to make use
of the machine throughout the year, one quarter lor adjustment seemed reasonable.

Students were asked to write four programs during the quarter with a fifth program
optional. Although programs were not counted in determination of the final grade, the class was
asked to turn them in for checking. About 80% ot all assigned programs were completed.

As an introduction to the machine, the first program was to determine all primes between
one and two hundred. This is a rather nice problem in that there are a number of ways in which
it can ue done, ranging from extreme brute force to relatively sophisticated sieves. Most
programs relied more on brute force.

Second was the old classic, computation ot the ged of two given integers via the Euclidean
algorithm. Carrying this a step farther, the third program asked for a solution to the
diophantine equation expressing the ged as a linear combination ot the given integers a and b.
Interestingly enough, rather than the usual procedure of unravelling the steps of the Euclidean
algorithm, it turned out to be preferable, for programming ease, to determine the convergents in
the continued traction expansion of a/fc (see [ 3 ]) .

ERLC

321

T ho last program was to determine the elements in i/(m) having multiplicative inverses.
This provided a ‘practical application* for one of our classroom theorems and also a family of
examples to he drawn upon later in our study of groups.

belated to this was an attempt to use the computer as a Gaussian pencil, furnishing new
data from whicn new discoveries can be drawn. A program giving the value of Euler#s phi function
tur integers between one and five hundred was stored in the machine. After typing in various
values of m and obtaining the values m) , students were asked to conjecture a general formula
for 0(m). Tnis was not as effective as had been hoped. Most students failed to observe the
multiplicative nature of ? despite a number of strong hints. Apparently a bigger push in the
right, direction was needed.

A fifth progra.-i, finding the Cayley table for the group of units in 2/(m) , was optional.
Because of the difficulties in formating the output, this presented the greatest problem, even

to the best students.

on a tew occasions students seized the initiative in using the machine. One group became
interested m Pythagorean triples and presented a report ot the class which included a program
they wrote to find all primitive triples with certain bounds.

out plans for the current quarter also include the computer. In class, we expect to do a
bit more group theory, study polynomials and then begin linear algebra. Programs we anticipate
assigning during the quarter are as follows:

First, determine the orders of all elements in the group ot units in 1/ (m) • By utilizing
earlier wotk, this program should be easy to write. It should provide experimental data that
students can use in considering the relationships between orders of elements and the order ot
the group.

Second, determine the gcd of two polynomials in Qf x] , where (Q) denotes the tiela ot
rutionals. This snould help draw the analogy between integers and polynomials with coefficients
in a field. In addition, programming the computation might help some students recognize the
general form of coefficients in products, something that might not have occurredit their earlier
exposure to polynomials stressed only numerical computations.

Third, determine all monic irreducible polynomials of degree less than m in 7/(p)[x] tor
given prime p and given m. Here we expect to make use of the exclusion principle - using the
lists of monic irreducible polynomials o£ smaller degree to construct all reducible products,
tnen excluding these from the list of all monic polynomials of the fixed degree. These
irreducib les will be of value later when we study field extentions.

Finally, determine the Hermite normal form of the augmented matrix for a system ot linear
equations with coefficients in the reals (sometimes called the Gauss reduction process). Systems
of linear equations occur in so many contexts in linear algebra that the utility ot the program
is juito apparent. In addition, past experience has shown that some students never recognize the
fact that there is a systematic procedure for finding solutions ot these systems or equations.
Programming tne procedure should impress its algorithmic nature upon their minds.

In summary, oul use of the computer has had several functions. First, tne student gains a
jetter understanding of material when he has to write a program. In this sense, programs have
the same purpose as problem sets. Second, the computer acts as a Gaussian pencil, providing
experimental data from which students can increase their fund of examples and make conjectures.
Third, the computer serves as a labor saving device, performing computations that would be
tedious and time consuming if done by hand.

Initially some students (primarily those without programming experience) found working on
the computer a bit distasteful. However, we feel that the pedagogical value, togetner with the
fact t'.at experience with computers is an asset in the competition for joor under the present
economic conditions, makes the frustration and labor oh* the part ot the student worthwhile.
Despite their reservations, students have been willing to try programming ana by and large we
feel tnat our use or the computer has been successful.

REFERENCES

1. Com£Ut.ers in Algebra and Number Theoryr SI AM - A MS Proceedings, volume 4 (1972).

I , io na 1 F r ob _lem s iqi Abstract A bra , ed i ted oy J. Leech, Pergaoon Press, 1 y7 0.

J. ill introduction L2 iii£ of ^li^bers , I. Vinogradov, Per gamon Press, l-JSS.

322

Program for finding integers x and y such that for given 2. Program for finding the units in */(m)
integers a and b (with 0<b<a) ax+by = gcd(a,b)

-O

-C

■M

4-1

if a*S(l-l) - b*R( 1 -1 )>o then put 1 i s t (S(l -1 ) , 1 - 1 R( 1 -i ) )
put 1 istC-'Sd-D^Rd-l))

A TIM E-S HARI .1 G COMPUTER IN THE DIFFERENTIAL EQUATIONS COURSE

Allen D. 2 iebur
state University of New Tort
Binghamton, New York 1J901
Telephone: (607) 79H-/M47

lattsiJisUaa

Since mathematics deals with numbers, it is obvious that the digital computer has a role to
play in teaching it. To many paople, that role is simple; let the iachine grind out answers to
■practical" problems. This article describes a course we have developed over the last half-dozen
years, in which we stress a different way to use the computer. Our iachine does grind out
answers to problems (we are not interested in the programmed learning aspects of CAI) , but these
problems are not supposed to ba " pra ct ica 1. * As in any math course, our probleis are designed to
deepen the student’s understanding of the theory we are trying to expound.

We therefore think of the computer as a device for teaching fundamental concepts. For
axample, a function is a set of pairs of nuibers, and a iachine can spew out hundreds of pairs
of numbers in the twinkling of an eye. An integral is a number, and because a computer can
integrate "anything" a student should get the feeling that "anything" is integrabie. (This
remark isn’t as foolish as it sounds. How many students come out of a standard calculus course
believing that the equation f(x| = e’x^ defines a non- integrable function?)

In tiacy ways, a course in differential equations provides an ideal setting to test this
philosophy of the computer’s rale as an educational tool. Traditionally, it is here that a
student "really" learns his calculus, tad the subject provides many opportunities to calJ on the
computer to aid in this endeavar. We have interpreted the content of our course quite liberally.
Before solving differential aquations, we solve some numerical equations, thus giving us a
chance to bring in Newton’s Hethod, for example. And since many differential equations are
solved by integration, it is natural to introduce Simpson’s Rule, and so on.

As for differential equations themselves, their solutions are functions, sets of pairs of
numbers. It makes a student rrally believe existence theorems when he uses, say, the Runge-Kutta
Method to generate a set of pairs of numbers that constitutes a subset of the solution of a
given initial value problem a n 1 realizes that he could do the same thing for "any" initial value
problem. We define certain functions, such as Bessel functions, as solutions of initial value
problems. The trigonometric functions could, of course, be defined in the same way, and a
student who produces a table of values of the Bessel function Ji by the same techniques he has
just used for the siae function is less likely to stand in awe of Bessel functions than is one
who thinks that mathematical tables are delivered by the stork.

Practical reasjus also argue for introducing the student to the computer in the
diffarantial equations course. Por one thing, it has a smaller population than the calculus
course, so less machinery - a 1 ministration plus hardware - is needed. Furthermore, there isn’t
a lot of extra time in the introductory calculus course, and it’s hard to fit the computer in.

Some Details

what made our course possible was#the invention of the time-sharing computer, and we have
usad several time-sharing systems over the years. la 1965-66, we had a Teletype terminal tied in
by long distance phone lines to the Dartmouth computer. With its beautiful language BASIC, that
system was simplicity itself, ind students were writing meaningful programs with only an hour or
so of instruction. Then wa used a remote access system (RAX) with PORTRAN on our own Model
363/40. To my surprise, its coiplicated software and hardware (IBf! 1050 terminals) didn’t seem
to bother the students. later, we had a much simpler time-sharing system (ITF) on a Model
363/57, and we shifted back to BASIC. We have also run the course using APL. Actually, our
programs are so simple that the particular computer system being used doesn't seem to make a
great deal of difference. Familiarity with the computer is not a prerequisite for the course;
we start from scratch.

Perhaps because it is my native tongue, I prefer BASIC. It and PORTRAN are so close to
ordinary mathematical notation that little time is wasted learning thei. The same cannot be said
for APL; one has to count on sacrificing * good deal of time to teach the language it he wants
his students to write programs of their own. (And the conflict between the notation and
terminology of APL and mathematics doesn’t add anything to the learning process.)

Specifically, our one-saxester course contains the following computer-related topics,
handled more or less as you woald expect them to be:

1. Solving numerical equations (using, for example, Newton’s Method)

325

define G(u)
x= y-z =o

G(U) = I/(I + U*U)

x *0

Y*o

z-o

WRITE (6,1) X,Y
I FORMAT (I X.F 3.1, F 10, 4)

DO 2 1 = 1,8
DO 3 J* 1,3

S«G(Z) + 4*G(.25*Y+,75*Z)
+ 2*G (.5*Y +.5*Z ) +
4*G(.75*Y +.25*Z)+G (Y)
R«-,I-K(Y-Z)/I2)*S
Y= Y-R/G(Y)

3 CONTINUE
Z = Y
x* X+ .1

WRITE (6,1 )X,Y

2 CONTINUE
STOP
END

FIGURE 1

2. Functions cod functions defined by integrals (such as x,n)

3. Initial value problems solvable by integration (linear, variables separable)

4. Existence theorems (based on Euler-Cauchy polygonal approximations)

5. flaking tables of vilues of functions defined by initial value problems (using Runge-
Kutta, Milne)

6. Series solutions of differential equations (trigonometric functions, Bessel
functions, Legendre polynomials).

These topics are interspersed rfith other standard material of differential equations, for which
the computer is used only sligitly, if at all. Thus, we also treat systems of differential
equations, linear differential equations of the second order, and so on. In general, computer-
related exercises are used whei they seam natural, pencil and paper exercises when they seem
more appropriate. More details are given in the book[ 1 ] that grew out of the course, which
happens to cover essentially tiose topics listed in [2, pp. 33-34].

An Example

This example is one o£ our most coaplicateu ones, but it serves to illustrate what we ate
tryin j to do.

•y

Example. Solve th^ initial value problem (1) y1 « 1 * y* and y = 0 when x = 0.

The giver di Iferential aquation is separable, so our theory tells us that the solution of
problem (1) is defined by the aquation

(2) /Vfr “ *dv ■

0 1 o

Thus, to make a table of values of the solution for x in the set 0, .1, ..., -8 , say, we must
solve eguatien (2) for y as x varies from . 1 to .8. For convenience, we have written G (u) = 1/(1
♦ u*J) in o'U- flowchart and FD.1TRAN program, so equation (2) can be expressed as

R(y): =* / G(u)du - x - 0 .

A little calculation shows that

R(y) = -.1 + / G (u)du ,

where z is the solution of equation (2) that we calculated on the previous trip around the outer
loop. Me solve equation (2) by Newton's Method, evaluating the integrals that arise by Simpson's
Rale. [Notice that the Fundamental Theorem of Calculus is used to show that R' (y) 55 G(y).]

As the example shows, our goal is not at all :o teach numerical analysis. The choice of
three steps for Newton's Method and four subdivisions for Simpson's Rule, for example, was
purely arbitrary. There is no claim that we have an efficient nuierical method for solving
problem (1) (of course, we also solve it by fiunge-Kutta, Euler-Cauchy and so on at other times
in the semester) * He are simply trying to illustrate what the method of separation of variables
really amounts to, drive home the fact that integration can be thought of as a direct (not; an
inverse) process, emphasize that numerical equations can be solved, and show once more that a
solution of an initial value problem is a set of pairs of numbers.

Naturally, we are not above such showman's tricks as having the student change the "write**
stateaert t o WRITE (6, 1)x,t ~TAN (x) • The results make him a true belie.er. Similarly, changing
the first statement to G(u> = 1/sqrt (1-u*u) and the "write" statement to WRITE (6 , 1 ) x ,y ,SIN (x)
produces an interesting table. It is in aaking on-the-spot changes like these, as well as
providing for iost anta neous correction of errors, that the realtime aspect of a t me-sharing
computer shows its value.

Student Res£onse

It is often hard to separate hoped-for results from real results, but a few educational
conclusions can be drawn. For one thing, almost all students do many more than the required
number of assigned computer problems. The weekly computer assignments are worded, "Do one or
more of the following problems." Practically no student hands in output on only one problem.

*>r;

* i P

327

students probioif do leave th» coarse believing that "any" function can be integrated aud "nay*
initial value problea has a solution, which I believe, too. (Became of our selection of
probleas, superficial treataeat of error analysis, and so on, students nay end up with tke falsa
iapressioa that producing correct nuaerical results oa a coaputer is siapler tkan it really is.)

The fact that coaputer prograas are tightly organised bits of logic is botk good and bad.
tf a student understands tke pcograa, he's got soaetking. If he doesn't, he*s got nothing*
Probably one can lose a student aore thoroughly via cosputer prograas tkan he can in a
traditional cookbook course in differential equations.

There is no doubt in ay aind that the coaputer can be an effective tool for teaching
traditional aatheaatics. after all, tke standard way to teach satk is via classroos exaaples and
hoaevork probleas. Tke power of the coaputer sakes available a auch wider selection of exaaples
and probleas than we had B. Z» our goal is to choose viseily froa these newly available exaaples.
That is easier said than done, of course, but it is certainly worth trying.

BXFEBBiCBS

1. Allen Dm Ziebur, id ESDi&iSBS* Dickenson, Cncino, California, 19 71).

2. ES£211SallUS>>3 t2£ *9 2i*SC3Ctams E£23£1I 19 £2ie3tlU3Bftl UUtllU»t i ESB2C& 3 i t&2
DABSl 2 9 £21£Jlii!l9# COPB, Berkeley, 1971.

330 328

THE ROLE OF THE COMPUTER IN REAL ANALYSIS

H. N. McAllister
Moravian College
Bethlehem, Pennsylvania 18018
Telephone: (215) 865-0741

In trod uct ion

• The Introduction to Real Analysis is an upper level course and is ottered every spring.
This paper outlines the objectives and the topics for which the computer is used in this course.

Ob ject ives

Moravian College has a Wang calculator with four keyboards and one card reader, a Textronic
model 909, an IBM 1130 and two teletypes connected with the CDC 6400 of Lehigh University. Wo
are also a recipient of a N.S.F. grant for a regional consortium for computer networks which
will last one academic year and two summers and which has the purpose ot training a number of
faculty members from various departments.

The Department of Mathematics has been and is actively looking for ways to make use ot the
computer in all of our courses. Last October we hosted a very successful all day workshop on
the Calculus and the computer to which we invited nearby colleges and high schools.

In our experience, the interest of the students is great and the computer shows that it can
represent a tool to increase understanding and motivation for applications to geometry, physics,
etc. Furthermore, the use of the computer adds significance to the theoretical aspects by:

1. numerically evaluating solutions of problems that one scarcely would have the time or
the patience to do by hand.

2. stimulating the student to independent thinking whether it is a numerical
verification of the truth of a statement or it is a construction of a counter-
example.

3. enabling the instructor to introduce in his course new topics very relevant to the
applicability of mathematics in modern fields which rely on the use of the computer.

The preparation of a major in mathematics is undergoing a drastic change. Because ot the
scarcity of jobs in secondary teaching, more majors in mathematics are looking for jobs in
business careers. Therefore the undergraduate education should train students with awareness of
applications of mathematics to a greater variety of fields than we did in the past.

Furthermore, many disciplines now require that their students take more courses in the
Department of Mathematics. The result has been a noticeable trend to have more mathematical
courses taught by non-mathematicians because we, mathematicians, are accused of not teaching the
kind of mathematics that is relevant to.the applications of the subject.

We believe that, at the undergraduate level, we should teach the beauty of mathematics not
only for its sake but also for the relevance of its applicability. In a narrow sense, we do this
already when, after having proven many theorems, we ask the student to prove something new,
thereby testing both the knowledge and the intelligence of the student. The course has been
dreaded for a long time by most students as they considered it too Mabs tract • ** The computer
provides again a tool that directs the student to use the information that we give him.

Examples

The above considerations led us to make some modifications to the traditional content of
the course. The purpose of this section is to indicate how and where the classical topics of
Real Analysis lend themselves to the use of the Computer.

The four examples represent just a beginning. The programs are written in FORTRAN. They
have not. been included but the FORTRAN listings of the canned programs tor examples (a) and (b)
are available to anyone who sends in a request to the author of this paper. The programs in
example (c) are written by the students. The program of example (d) is also available in APL
language and is due to Dr. W. Miranker, IBM, Res. Ctr., P.O. Box 218, Yorktown Heights, New York
10598.

329

331

Limits of a function of a real variable.

x^c .ft completely interactive program has been developed by this
author. It has been stored in the memory of the CDC 6400 and is available to all
colleges and high schools of the network. It is emphasized that the computer does not
provide the evaluation of the limit L, if it exists. The students need to define the
data, namely the formula of f (x) , c, the stepsizc h, the initial value of x and their
guess of the limit- L .

If L and c ar«* finite, the program requires a value of 5. The output consists of a
listing of values of x,|x-c|, f(x), |f(x)-L|. The computations will produce an

c?valuation of <5 , if any, for several numerical choices of G.

It L is finite but c is not, the output lists the values of x, f (x) and t(x)-L . The
computation will produce an evaluation of a constant fl *> () for each numerical choice of

If c is finite and L is not, the program requires a value of a constant N>0. The
output lists the values of x, f (x) , Jf(x)|. The computations will produce an

evaluation of <S for each numerical choice of N .

It l and c are not finite, the output li=!ts the values ot x, f(x), jf(x)| and the
computations will produce and evaluation of a constant MM) for each numerical choice
of N .

From the listing of values in the output many remarks can be made. For instance, the
output illustrates the necessity of different definitions for the limit of a
function. The theoretical dependence of 6 and <5 can bo verified. The function f (x)
= 1/(1 +e2) , with c = 0, is a good example of one-sided limit. If L is an irrational
number we may bring up the completeness of the real number system and a verification
of the Cauchy Criterion for a sequence of rational numbers produced by the computer.

Naturally, the limitations of machine computations arise like the loss of significant
digits due to round-off error.

Plotting.

A program plotting a function of a real variable over an interval [a,b] is available.

The program of example (a) gives the student the option to plot the values ot x and
f(x). The plotting is particularly effective when there is an asymptotic behavior.

In th# past, we used a few films to illustrate the convergence of a sequence of
functions fn (x) , n = 1, 2, ... it is a far superior teaching device to have the
students directly involved in plotting some of the functions in the sequence. The
plotting is automatically scaled, therefore it illustrates quite effectively the
difference between pointwise and uniform convergence.

Plotting some partial sums of a series of functions of a real variable is just as
ef feet i vs.

The fixed point theorem and successive approximations.

Several theorems are referred to as fixed point theorems. For sake of precision we
state it.

Theorem: Let S be a nonempty complete metric space, F: S— *S a function. If there

exists a real number L < 1 such that for all p, qSS we have

d(F(p) , F (q) ) < Ld(p,q) ,

then there exists a unique point P6S such that F (P) = P . Furthermore, for any p GS
and p =F(p 'j , n = 1, 2, ... we have lim p =P. 0

n n-1' n-yoo *n

This theorem represents a most powerful tool in mathematics. It is our object to
stress its significance by showing that many of the iteration procedures found in
nearly every branch ot applied mathematics are merely applications of this theorem.

330

332

Our presentation is intended to point out the power of a relatively simple theorem,
developed in a space whose elements are somewhat "abstract" and we do not aim at the
most general treatment possible.

We consider applications to the solution of equations of the type:

1. f (x) = o;

2. f (x# y (x) ) =0 for y <x) ;

3. Dxy = f (x, y (X) ) for y (x) .

We are still debating on whether to include next semester the solution of AX = 0,
where A is a linear, self-adjoint, positive definite operator from a Hilbert space
into itself, and to introduce the conjugate-direction method and the method ot
steepest descent (see chapter 1 4[ 6 ]) .

A gre.t deal of numerical computations can be made. For instance, for (1) we chanqe
the equation into x = F ( x) and we consider the methods ot fixed secant, Reg ula Falsi.
Muller, Newton and Chebyshev. We then turn to the problem ot convergence speed and a
comparison of the methods. For (3) we follow a unifying approach, see chapter b [U]
and we consider some simple predictor-corrector methods, e.g. Euler’s method and the
midpoint method.

d. Pattern recognition.

One of the problems in pattern classification is connected with the specification ot
an algorithm that, identifies a pattern based upon a set of numerical measurements
that represent the patterns.

The mathematical techniques that are needed to describe a model dealing with machines
which distinguish among classes of patterns are those of functionals, see chapter 3C,
D (3]« We give here only the outline of the linear model [2] which specifies an
algorithm to identify a pattern based upon a set of numerical measurements.

Let the space S consist of all possible patterns which may appear. We assume that
the space is partitioned in m disjoint subsets , ...» S^. For example, in

numerical character recognition we have 10 numerals. In alphameric character
recognition we have 26 upper case letters, 10 numerals, and a certain number of
punctuation symbols.

The sequence of n numerical measurements on each pattern is a mapping from S to En ,
the euclidean n-diraensiona 1 space. To each pattern weS we associate its vector x =
x (w) = (xi *X2 » • • • *xn) of measurements. We achieve a proper identification ot

elements in S provided that there are sufficiently many measurements to distinguish
among the sets , i = 1(1) m. The usual procedure is to partition En in m disjoint
subsets A1 , so that if x(u))eA^, then the pattern u>eSj is chosen.

Fol simplicity, we assume m = 2 in the following. Let

L (x) = (v,x) = v x + ... + v x ;

11 n n

A = {a./i=l[l)p} En ;

B = {bJ/j=l(l)q} En .

Notice that the linear functional L depends on the vector v. Two finitie subsets A
and B of £n are said to be linearly separable if there exists a linear tuncitonal L
such that

max L (b . ) < min L(a.) .

l<i<p 1

If there exists a number c such that

max L(b ) < c < min L(ai) ,

then the hyperplane {x/L(x)-c = 0} separates the pair A, B. The following theorem
gives the conditions on A, B to insure the existence of a separating hyperplane.

«' *

331

333

Theore m: If A and B are finite subsets in En , then A and B are separable if and only

if the intersection of the convex hull of A with that of B is empty.

He need now an algorithm that yields a vector v, a constant c and a theorem that
proves the convergence of the algorithm to satisfactory values for v and c.

Let the following natrices represent the elements of A and B respectively:

(A) - (a^), i-l(l)p, j-l(l)n;

(B) - (b±J) , i-l(l)q, j-l(l)n.

Let (A*) be the p*(n+1) matrix obtained from (A) by adding a column of 1, i.e. (A*) ■
(«}j) * («ii#ai2 # . • • #ain| 1) # i*1(1)p. In a similar way we construct the q« (n+1 ) matrix
(B*J. Notice that A*CEn+1 and B*ceh+1. Let T* equal any sequence of vectors chosen
from the set A*ub* in En+1. If we define w«(v^ ,V2 $ . . . #vn ,-c) then the condition (v,bj)
«c<(v,ai) j»1 ( 1 ) q # i*1(1)p becomes (w,b*K0<(w,a*) for all a*€A*, b*£B*.

Since A and B are finite sets there exists a number 6 > 0 such that

p (w, b*) < - Q < 0 < £ < (w , a*) .

The value of £ is arbitrary because if the above systen of inequalities has a
T solution for sole £ > 0 then by homogeneity it has a solution for any £ > 0.

Algorithm: Let £ > 0 and WQeEn+1 be chosen, the iteration is defined as follows:

? + t*

1 n

(w(n-1),t*)

< e-

J w(n-l)

£w(n-l)

> 0;

^ w(n-l) _
i n

(w(n"1),t*)

jyn-D

< -e j

and if t*eA*
n

and if t*eB*
n

Tfreoyea: The sequence {w^nVn = 1,2, ...1 converges. There is an integer N,
depending upon A*, B*, £ andwQ, such that w^N) * w(N+1) - ... If T* has the property
that each element of A*UB* occurs infinitely many times, then w(N) is a solution.

Notice that the algorithm yields wW as a linear combination ot the elements of A*
and B*; hence v is a linear combination of the elements of A and B. Prom the
magnitude of the coefficients of this linear combination we see which patterns are
relatively more significant for the purpose of separating the sets Sf and S2* He also
see from the components of v which measurements are least significant in the
classification and consequently can be dropped.

£2£L£l4£lons

No textbook is available with the outline and the emphasis that is desired. The students
are asked to purchase the book of reference [ 1 ] of which we cover chapters 1, 3, 4, S, 7. A full
set of lecture notes is given to the students covering metric spaces, the method of successive
approximations (see chapters 3, 8 of [5] and chapters 3, 4 of [3]) and elements of pattern
classif icaitons (see [2]). We do not cover any theory on integration as we do a rather decent
treatment of it in Calculus and in Advanced Calculus.

No figures are available with respect to the cost of computer time. The Administration does
not think it worthwhile to keep a budget that distinguishes among the number of hours of
computer use by each course.

334

332

The nuaber of students that have becoie computer Mbuis" is ainiaal as is also the nuaber of
students who considered the computer wort to be a burden.

REFERENCES

1. Geiignani, H. , Introduction to Real Analysis , 1971, tf. B. Saunders Coipany.

2. Greenberg, H. J. - Konheii, A. G. , Linear and Nonlinear Methods in Pattern Classification.
IBH J. Res. and Dev., B (1964), pp. 299-307.

J. KripAe, B. , Introduction to Analysis, 1968, U. H. Preeian Coipany.

4. Ralston, A., A P^rst Course in Nuaecical Analysis, 1965, HcGraw-Hill.

5. Rosenlicht, M. , Introduction to Analysj^. 1968, Scott, Poresaan.

6. Todd, J. , Survey of Nuierica l Analysis, 1962, HcGraw-Hill.

333

335

COMPUTERIZED HELP IN FINDING LOGIC PROOFS

Arthur E. Falk and Richard Houchard
Western Michigan University
Kalamazoo, Michigan 49001
Telephone: (616) 383-1659

We have a program in operation which provides students with critical advice on proving
i aconsiste ncies in guan tif icational logic[ 1 ]. The prograa adapts well to an extremely large
range of students’ responses, which are typed in the notation of symbolic logic. And it
compares favorably with a human tutor in his capacity of critic, both in the competence of its
advice and in the hourly cost.

QUINC (QUantif icational I NConsis tency) is novel in that it not only demonstrates
inconsistencies skillfully, but also helps students to do likewise by its constructive criticism
of their attempts. Some advice they receive depends on a comparison of their work to the
computer’s proof. Thus it is one of the few CAI programs which make significant use of the
calculative power of the computer, as contrasted with its record keeping capabilities. There are
programs which can prove difficult inconsistencies in quan tif icational logic (Robinson, 1967),
but we know of none but our own which assist humans in developing their skills to the same
level •

The objectives of a one semester course in symbolic logic include not only the presentation
of information about logical theory and its applications, but also the development of the
student’s skills in translating ordinary discourse into schemata written in the notation of
logic and his skills in demonstrating the inconsistencies in sets of inconsistent schemata. The
methods of teaching the latter skills are classroom demonstrations with much studen t- teacher
interaction and written homework assignments- Both methods are economical compromises permitting
the instructor to give some individualized attention to students while still maintaining a large
number of student-hours of contact- The teacher in other words is a time-sharing system. But
class time spent doing many illustrative demonstrations is time lost for the presentation of
further applications of logic. Our prograa takes over a part of the job of presenting
illustrative demonstrations and guiding the student's own attempts- In this way we save two
weeks of class time for the presentation of additional applications of logic, thereby enhancing
the usefulness of the course to the students. As for written assignments, they are tedious to
correct in great detail, and consequently are not prescribed frequently enough. Their value is
also lessened by the great delay between the students’ writing them and their receiving them
back corrected- These particular deficiencies of written homework can be overcome if the
student does his assignment on a teletype connected to a time-sharing system with a prograa like
QUINC. The result is immediate and frequent advice tailored to his own response, replacing
delayed illegible, often cursory (albeit individualized) homework corrections. QUINC’s advice
is immediate; the program watches over the student’s shoulder, so to speak, as he works. It is
frequent; almost every response the student makes is commented on. It is tailored to the
student’s response; the prograa can offer the student more than sixty different pieces of
advice on appropriate occasions. *

QUINC remains useful to students even after they have mastered the procedures for
demonstrating inconsistencies. For the procedures become cumbersome when applied to more
advanced problems. However, with QUINC they can work out a proof quickly, leaving the tedious
calculations to the computer. This permits much more extensive use of theorem proving in the
exploration of axiom systems and formalized theories.

The program does not do many of the things we associate with CAI programs. For example, it
does not choose or sequence the problems to be done by the student. That is left to the student
or teacher. Nor does the program evaluate the over-all performance of the student. The teacher
does this by administering tests of course, but also by examining printouts he receives of each
student's interaction with the computer. The prograa is not meant to put across new course
content. We assume that the student has already learned the notation system, its interpretation
and the rules and stratagems for discovering inconsistencies. The prograa helps the student to
orqanize what he has learned by bringing it to bear on problems successfully in closely
monitored practice sessions-

The prograa does what it is supposed to do fairly well. It compares favorably with human
advice-giving, both in cost and in competence. The prograa uses 19K of core of a PDP-10. On our
system costs average $4.75 per hour of connect time per student. This is higher than the cost
of an instructor's demonstrating inconsistencies in class and correcting written homework- But
it is about the same as the prevailing rates for tutoring (in the sense of 'assisting in
remedial studies,' a form of work often undertaken by successful students)* Although the
prograa does give bad advice on occasion, it is competent enough to warrant comparison to a
tutor, at least in his capacity as critic of student's responses. Seventy-five students used
the program for three weeks in their intermediate logic classes. At the beginning of this three

week period they were given fifty inconsistencies, graded intuitively into five levels of
difficulty!; 2 ]. The students were told that they aust reach in three weeks a level of coapetency
to insure that they could demonstrate inconsistencies of the fourth level of difficulty. The
students then worked at the teletypes on as aany of these problems as they felt necessary. No
class tiae during this period was devoted to deaonst rating inconsistencies except for a very
siaple one illustrating three stratageas. No hoaework concerning demonstrations was corrected
by the teacher during this period. Then the students were tested on a problea of level four
difficulty. Depending on the particular problem used, between one-half and two-thirds of the
students demonstrated the inconsistency without error. In the light of the instructor's past
experience these results are aore than satisfactory. But the average student was not guite as
enthusiastic as the instructor, When the students were asked, NHow helpful has the computer been
in teaching you to prove inconsistencies?11 they rated it at 2.5 (or C + ) on a 5 point scale froa
4 ("extremely helpful") to 0 ("no help at all"). Soae of the problea was that they encountered
annoying bugs in the prograa. Another part of the problem can be traced to the tine-sharing
system, for when asked, "How much of a hindrance has been the waiting for teletypes and computer
connections, the delays in answers and garbled messages?"- 4 ("very nuch of a hindrance") to 0
("no hindrance at all") - they rated the hindrance due to the system at 2.5 also.

The rest of this paper will describe the sequence of events that occurs when the student
interacts with the computer. The description is divided into three parts, (A.) Preliminary
steps, (B.) The coaputer's denon stration , and (C. ) The student's demonstration.

A. Preliminary ste£s. The student calls for tfUINC and, after introductions, receives
any aessage that the instructor has inserted under his project, programmer number. This message
is for that student personally and is based on the instructor's examination of the printouts of
the student's previous work (Fig. 1, a). Then the student types the quantif icational schemata
he wishes to test for inconsistency (Fig- 1, b) • It he wants to test for soae other
characteristic such as validity, implication or equivalence, he can do so indirectly, for he has
learned how to convert these tests into tests of inconsistency. Thus he knows that to test a
schena for validity, he aust test its denial for inconsistency. He knows that to test whether
one or more schemata imply a certain schema, he oust test the set of scheaata consisting of the
preaise schemata and the denial of the conclusion schema for inconsistency. For we understand "£
implies g" as "j> is consistent with the denial of g. " And to test if two scheaata are
equivalent, test if each implies the other. Thus tests of inconsistency can be used to determine
all the standard logical relationships.

In typing the scheaata to be tested, the student nay use syabols for the existential
quantifier, ($X) , (SY) , etc., which are read "soaething is such that"; for the universal
quantifier, (X), (Y) , etc., which are read "everything is such that"; for negation, -, read "it
is not the case that"; conjunction, . , read as "and" or "but", parentheses, and predicate
letters (A through L) followed by up to four variable letters (N through 2) . Other connectives
such as "or" and "if" can be put into the notation with just these syabols. Deviations from
standard symbols, such as $ for 3 and capital letters for variables are forced on us by the
teletype keyboard.

Ve can construct an English interpretation of the first schema in Figure 1 by reading F(1st
variable) (2nd) as "(1st) supports (2nd)," reading G(1st) (2nd) as "(1st) loves (2nd)," and
letting our universe of discourse be persons, that is, we read quantifiers as referring to
persons, for example, we read "someone" rather than "soaething." The schema is then interpreted
as, "Soaeone is such that ♦ everyone is such that * the latter supports the former ♦ but ♦ it is
not the case that + the latter loves the former." Bore colloquially it says, "Soaebody has
everyone supporting bin without love." The second schena (Fig. 1, d) is interpreted as "It is
not the case that ♦ everyone is such that ♦ soaeone is such that * the former supports the
latter," or "Not everyone has soaeone or other whoa be supports."

After the student has typed in the schemata to be tested, the computer evaluates thea for
proper construction. If they are ill-formed or exceed the limitation to four variables
following a predicate letter, the student is told what error he has aade and where it occurs.
Nine different errors are diagnosed for the student (Fig. 1, c). The student is then given an
opportunity to correct his aistakes (Fig. 1, d) •

If the student's scheaata are well-formed, the program checks then for prenex fora. A
schema is in prenex fora if all its quantifiers are the leftaost symbols in the schena, each
governing the whole of the schena to its right. Before an inconsistency check can be carried
out, every schena must be put into that form by following certain rules. The computer does this
for the student. All steps in the derivation are typed out (Fig. 1, e).

The progran then searches for a proof of the inconsistency of the prenex scheaata. If the
conputer cannot find any inconsistency, it tells the student that it cannot be of any service to
hia on that problea. Bore often than not, if the coaputer cannot prove an inconsistency, it is
because the student did not type the schemata he intended to. There are therefore procedures
for correcting typing errors at this point, When the corrections are completed, the program

336

• it H DiK J JI MCC63001 #63030:)

HELLO • Ai MAME lb HA L. bOMEOAT I HOPE f) ^ A bP ACE
PILOT. I M THE MEAMTI1E I ' A CQMTEMT TO HELP TO J rfX TH TO Jn
L 0 3 1 C • */HAI bHO JLl) I CALL TOO?

MOLLT KLlSMJSb
HELLO# *1 OL L T •

LAjT i 14 1£ TOO DID bEOEHAL LEVEL 1 JO PaOBLEM;# JltHOJl A NJ T
MlbiAKEb* JHT MOT THT SOME LEVEL THHEE PrtOdLEMS f )DA T ?

I'4 HEAD T TO HELP TO J TEST SOME bCHEMA 1’A FOi< I MCOMb I b TE Ml) T •

THE DI HECTIOMS FOa TTPlMi SCHEMATA Alt I M .JMIi 60.

(BAH THFTa.-OTA)

-< A ) ( f >F£ J

cCHK^lA a* THE EaI S TEMf 1 AL MUAMTIFIS:* DOES MO i* COMTAIM A VAKIABLF.
-<zlX:fi)F£.J

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HO HO HO AH# TES# MOLLT# VHT DOM'T TOJ MOV TTPE THE

VJvldEH OF THE IMCOHKECf LIME# rtKfUliM* 4 I«LL TTPE “OK"# THEM
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-(DCS J)F<W
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I'LL CHECK FOit P HEME A OhOEh AO 4* MOLLT.

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Figure X

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338

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figure 2

338

redoes its work, deriving prenez equivalents for the re-typed schemata and searching for an
inconsistency. If an inconsistency is found, the proof is stored, and the student is told to
proceed, without being shown the proof. But at least he is assured that the computer has found
one (Fig- 1, f ) . It is also possible for a student who has mastered the proof procedures to yet
the coaputer to chock out a proof which it cannot itself do.

Up to this point in the prograa there are twenty different responses that the prograi can
■ake to student inputs, not counting the endless variety of responses involved in the derivation
of prenez for as.

B- T he coaputerls proof: If the conputer's advice is to rise at all above the utterly

basic and jejune, it Bust solve the problea for itself. Creating a prograa to do this is no

snail task. The sethod of denons tra ting guantif icational inconsistencies belongs to a class of
nethods which involve two sets of instructions, first, rules defining legal steps, and secondly,
heuristic stratagens characterizing effective steps, that is, steps that probably expedite
reaching one's goal. The stratagens are needed because at any stage in the solution only a very
few of the legal steps would actually be effective. Faailiar illustrations ot this distinction
are ganes like chess and checkers. The difference between a "wood pusher" and a aaster is not
in their knowledge of the rules, but in the heuristic stratagens they follow. An analogous
situation occurs in quantification theory in proving inconsistencies. The stratagens are
"heuristic" relatively to the class of problens which we attenpt to solve and are solvable. That
is, they frequently help us, although not always, and without then we would rarely succeed in
finding a solution in a reasonable anount of tine. No fixed nuaber of stratagens is ever
perfectly reliable, unless the class of problens we attenpt to solve is restricted so as to

insure solution by just these stratagens. But if we do not arbitrarily linit problens in this

way, we find that there is no upper bound on the degree of ingenuity and nastery one nay show in

producing inconsistency proofs. Prograaaing a computer to exhibit a high level of mastery in
this area is as challenging as it is in the areas of chess and nedical diagnostics.

The rather inelegant algorithn we have cone up with resists brief, exact description- It is
best approached by way of an illustration. The coaputer solves the problea in Figure 1 in the
following manner.

1. There's soneone whom everyone supports but doesn't love. $X) (Y) (FYX.-
GYX)

2. Somebody supports nobody. ($Z) (U)-FZW

These are the prenises which we wish to show to be jointly inconsistent. Intuitively, if someone
is supported by everybody - literally everybody - he even supports himself, and so 1. is
inconpatible with 2. The deaonstration consists of replacing successively the quantifiers
"soie,H "every," and "no" with nonce naies. The unbound variables H and N as they occur in the
following steps should be thought of as nonce naaes like "John Doe" and "Richard Roe."
Quantifiers in a single schema nust be replaced in the order in which they occur. The
replacenent process is called instantiation.

3- (from 1 by instantiation for "someone") Let's call the one whom everyone
supports but doesn't love, n. Everyone supports, but doesn't love, n.
[t) (FYH.-GYH)

4. (fron 2 by instantiation for "sonebody") Let's call the one who supports
nobody, N. N supports nobody. (U)-PNW

It would have been illegal in step 4 to use M again, for it would be tantamount to Baking the
unsupported assumption that one and the same person supports nobody but has everyone supporting,
though failing to love, hi«. (Of course N nay or may not be the sane person a s a just as in
legal argunents "Bichard Boe" Bay or nay not be the sane person as "John Doe.") It would have
beer, leqal to produce an alternative to our current line 4 by replacing the "everyone" of line

3. But such a line, though legal., would have been useless in denonstra ting an inconsistency.
Theis we have a sequencing stratagen which helps us avoid such lines. It requires that
existential quantifiers be replaced as early in a demonstration as is legally allowed. But after
produced our current line 4, our best line 5 is the very one we rejected as an
alternative fourth line:

5. (from 3 by instantiation for "everyone") Since everyone supports, but
doesn't love, H, it follows that: N supports, but doesn't love, 8 FNM.-
GNfl

The rule for replacing "every" peraits any nonce nane (other than letters appearing in further
quantifiers on the line) to be used, whether or not it had been used previously. To deternine
which of the aany nonce nanes pernitted is the one nost likely to help us derive an
inconsistency we have developed the Batching stratagen. The Batching stratagen requires that one

34 0

so choose his nonce naies so that the atoms created in quantifier-free lines natch one another
to the greatest extent possible. An aton is a component of a schesa consisting solely of a
predicate letter followed by variables. It has no quantifiers, negations, or conjunctions in it.
Thus FNH is an aton; so is GNH. Before we chose N in step 5, the natching stratagen directed us
to note that in step 4 P is followed jy the nonce nanc H. The choice of N again is a step toward
creating natching atons beginning with P. Note that the sequencing stratagen followed in step 4
facilitated the use of the natching stratagen in step 5.

This also illustrates the natching stratagen. At this point there are no further quantifiers to
be replaced* so the conputer perforns certain truth table calculations. In effect it ascertains
that the conjunction of the quantifier-free lines 5 and 6, FBH.-GIIH--FNH , is self-contradictory.
Since the quantif ier-f ree lines that were derived fron our prenises are inconsistent, we have
denonstrated the inconsistency of those prenises. If the conputer had failed to denonstrate an
inconsistency at this point, with sone problens having certain characteristics it would have
produced further quantifier-free lines by naming alternative choices of nonce nanes, in
obedience to the "never- say-die" stratagen. However its obedience to this stratagen is perforce
United. It is linited to insuring, first, that ail atons with variables free either originally
or as a result of dropping existential quantifiers natch at least one other aton. It would then
perform the truth table calculations over, taking into account the new as well as the old
quantifier- free lines. If they are still jointly consistent, the conputer would continue
deriving new lines which now, however, nay only have atons which natch previous atons. These
lines are checked against the truth table, and useless ones are discarded* If after this the
quantifier-free lines ar« still consistent, the calculations end.

Our algorithn for doing proofs is not as straightforward or as elegant as we would like,
but we had diverse criteria which we had to meet. And the nonster we created net each
criter ion.

First, this proof procedure we use is easily taught and justified to students. The rules
defining legal steps are enployed with only trivial differences in sone excellent elenentary
logic textbooks, e.g., Quine (1965) and Jeffrey (1967). In order for the progran to work, it
must- siaulate the proof procedures that the student is to master for the prograaned advice ains
to have the student enulate the conputer9s way of doing things.

Secondly, this proof procedure represents an acceptable compromise with the nethod nost
adaptable to computerization, which unfortunately is not so easily taught or justified to
students (Robinson, 1965). our ain was to employ stratagens powerful enough to succeed on any
problem used as an illustration or assigned as an exercise in any elenentary logic textbook. Be
have tested it on a variety of problens fron Quine (1959) M965), Suppes (1957), Sates (1965),
Lewis and Langford (1959), and others. It did all problens involving nonadic predicates
(although we have constructed sone that it cannot do). It has done nost problens involving
dyadic predicates, for exanple, the theorens in Sates1 theory of the syllogisn, and Suppes*
theory of rational preference, and the problens in Quine (19L9) concerning the properties of
dyadic prea^ ates. Hates and Levis and Langford present theories of betweenness and separation
of point pairs on a circle which involve triadic and tetradic predicates respectively. The
progran does not do nearly so well as it does with nonadic and dyadic predicates. Our version of
the natching stratagen is not the optinal one for these problems. Be are satisfied, however, the
progran can do practically all but the nost advanced problens to be found in elenentary logic
texts. Although it has narginal value as a research tool, it can be used to illustrate the
application of logic to elenentary scientific and nathenatical theories which employ the
axionatic or hypothetico-deduc tive method and which do not require operation symbols for their
convenient formalization.

Be also compared QDINC to oth^r theoren proving programs. Ours is probably not as powerful
as those developed as research tools. Be can prove an inconsistency using Pravitz's (1960)
illustrative schema with tetradic predicates and also those reported by Davis et al. (1962). But
we cannot prove the inconsistency of:

first attempted by Gibson (1960) and eventually solved by the programs of Davis et al. and
others, but even these programs are manifestly inefficient compared to the human who, by taking
some thought, can denonstrate this schema's inconsistency by deducing just five quantifier-free
lines fron it. our problem was not simply to demonstrate inconsistencies, but to denonstrate
them in a way worth having a student emulate.

Thirdly, since the student must wait for the progran to prove an inconsistency before he is
allowed to proceed, the proof procedures must succeed in finding a proof in a brief span of tine

6. (from 4 by instantiation for "nobody") Since H supports nobody, it
follows that: M does not support a-FBrt

(x) (y) ( a z)— (- (Fxy.— (Pyz.Fzz) ) .- (Fxy.Gxy.— (Pyz.Gzz) ) )

340

or else coie to an end. This cost us such power in our proof procedures. The search for a proof
will terminate if more than twenty different atoas are created in quanti f ier-f ree lines. But we
have been successful in Uniting the expenditure of tine. The average student has to work at the
teletype for one hour before he uses thirty seconds of runtine. Total waiting tine at the
teletype during peak hours of conputer usage following the production of the prenex forns until
the student is given the go-ahead is frequently inperceptible even for conplex problems. When
noticeable delays do occur, they are as likely to occur at any point in the progran as at this
one. They are caused by having to share the conputer's tine with nany other users.

C. The student »s proof. once the student is given the go-ahead, he is to proceed in the
sane way as the conputer did, or at least in roughly the sane way. He types in a line and
identifies the line fron which he derived it. The conputer then responds to it with one or more
of forty different replies, either rejecting the line or accepting it and nunbering it. It
accepts any legal line the student types (except in nost cases exact duplicates) and allows any
seguenci g of the^. It rejects illegal lines; ten responses explain the reasons for rejecting
lines ig. 2, b) . They are independent of the conputer's own proof. Indeed there would be no

need fc the progran to actually do a proof if all it had to do was to connent on the legality
of th student *s lines. But in view of the fact that one can derive an endless series of legal
lines and never get close to proving an inconsistency, a tutor who could not advise on
stratagens for producing effective lines would be nost exasperating. The conputer's own proof
is essential for the conputer's advice on stratagens (in addition to insuring that an
inconsistency is present in the first place and in supplying the student at the end with a
conparison to his own effort or with a nodel, should he reguest it). If a line is accepted it is
either praised or criticized for violation of the stratagens (Fig. 2, a and d) . Thirteen
comments concern this, of which ten are alternative reaarks of praise (Fig. 1, h; Pig. 2, c, e,
f ) . The praise given is occasionally undeserved since the conputer gives it whenever a student's
line nat> hes one of its own, and it occasionally produces lines that are useless.

A ikd jor dilenna in designing the advice on stratagens was that on the one hand it had to be
geared to the conputer's way of proceeding, but on the other hand there are nany alternatives,
equally elegant, ways of demonstrating an inconsistency, any one of which nay be opted for by
the student. Unless sole unobjectionable way was found to coax the student into doing the proof
as the conputer did, the advice he would receive would be less than useless. Our solution was to
allow the conputer to sonetines change the students choice of variable letter in a legal line.
This facilitated conparison of the student's proof with the progran4 s considerably. In two
situations the progran changes the student's variable to one that is used in its own proof. In
these two situations the student's (and the progran's) choice of letter is arbitrar y[ 3 J.

Whenever the student's choice ought to be notivated by the natching stratagen, no substitution
is made. So the progran's substitutions will never create Batching atons for the student (nor
will they change illegal lines to legal ones).

If the student wishes to persist in his own choice of variable, he can do so sinply by
epeating the line with his original choice of variable. Unfortunately such creativeness

(stubborness) causes a serious erosion of the quality of advice on strategies. If he persists
and nanages to avoid confusion fron the mounting tide of bad advice, he nay still produce his
own idiosyncratic proof. The progran will then vindicate the student's procedure by confirming
that he has indeed found an inconsistency.

There are two other situations in which QUINC changes the student's chosen variable. If the
program has used a certain variable in dropping an existential quantifier, and the student tries
to use that sane variable without motivation in another context, and a change to the program's
choice in that context would not produce a line duplicating the program's, then the computer
changes the student's choice to a letter that occurs nowiere in the program's proof. This

situation occurs when the student works from a line already different from any line in the

progran4s proof, so that no matter what he does, a duplicate of the computer's lines cannot
result. In this situation the best that can be done is to at le^st keep open the possibility
that eventually he will start producing duplicates of the computer's lines. Thus the program
saves the variable for that eventuality.

In this situation the substitute lines which the progran foists on the student are neither
more ; ar less useful than the lines they replaced. From the programmer's point of view they are
both bad since the computer cannot give good advice concerning their use. Consequently the
student is warned that the computer's proof does not contain them, and that his success most
likely lies in ignoring them and taking an altogether different tack. The hope is that he will
then suggest a line which duplicates one in the computer's proof or which can be changed into a
duplicate by use of the saved variable.

A student cannot get his own way in these cases sinply by persisting in his choice. The
program will continue to replace his choice with previously unused variables until the supply
runs out. If that happens, work on the problem terminates with one of two breezy responses. But
the student can refuse the hint to ignore the substitute line and continue to work fron it. As
in the other cases, this has a very deleterious effect on the quality of the advice on

341

\ * >

v v »

342

stratagems, although there is one response that can occur at this point vhich warns him of this
fact. If, despite all, he finds an inconsistency, the prograa will vindicate bin by verifying
his result. J

All this creates the iapression that the student's proof aust exactly duplicate QOINC's.
This is not always the case. When the stratageas allow alternative line sequences, the student
nay sequence his lines differently fron the computer's, and he won't receive any flack for doing
so (Fig. 2, student's lines 7 and 8). The student also cones in for special praise if he
denonstrates an inconsistency in fewer lines than the conputer did. This can happen if the
conputer derives unnecessary lines.

There are several ways in which QUINC progresses froa one problea to another. It the
conputer cannot find a proof, the student is invited to revise his preaises or begin another
problea. If, however, the student has been allowed to proceed, the noraal way of ending work on
a problea is for th^ student to type INC ("inconsistent") • The conputer at this point obliges by
doing the appropriate truth table calculations. If the student is correct, the conputer
acknowledges this with one of three responses {Fig. 2, g). It types out its own proof and
invites the student to try another problea. If the student is wrong four tines in typing INC,
work on that problea is ended without the coaputer's proof being shown, but the student is
invited to do another problem. If the student does not know how to proceed, he can type MAC
("machine"). The machine then gives its proof and invites him to make another attempt.

FOOTNOTES

1. We gratefully acknowledge our drbt to Ns. Tenho Hindert for the original suggestion and for
auch help along the way, and to the Western Michigan University Computer Center for its
unstinting donation of services.

2. F*f th level; the dyadic problems from Suppes and Mates (see above, p. 10); fourth level;

( a x) ( 3y) (z) - (Fxy. Gsy. - (Fyz* Gzz) ) and others; thi;:d level: the problem in Figure 1 and
others; second level: syiiojisms.

3. Either the student dropped an existential quantifier, thus choosing a variable not
previously used (Fig. 1, g) or he dropped a universal quantifier when no possibility exists
of his creating acorns matching atoms in other lines, and the same is true for the duplicate
line in the computer's pro'*.

REFERENCES

M. Davis, G. Logemann, and D. Loveland, "A Machine Program for Theorem Proving" Communications
of the Association for Computing Machinery , 5 (1962) 394-? 97.

P. Gilmore, "A Proof Method for Quantification Theory" IBM Journal of Research and Development.
4 (I960) 28-35.

R. C. Jeffrey, Formal Logic: It^s Scope arjd Limits (N.Y.: McGraw-Hill, Inc., 1967).

C. I. Lewis & C. H. Langford, Symbolic Logic . 2nd ed. (N.Y.: Dover Publications, 1959).

B. Mates, Elementary Logic (N.Y.: Oxford University Press, 1965).

D. Prawitz, "An Improved Proof Procedure" Theoria 26 (1960) 102-139.

W. V. 0. Quine, Methods of Logic, rev. ed. (N.Y.: Holt, Rinehart and Winston, 1959).
, Elementary Logic . rev. ed* (N. Y. : Harper and Row, 1965)*

J. A. Robinson, "A Machine-Oriented Logic Based on the Resolution Principle" JournaJ of the
Association for Computing Machinery. 12 (1965) 23-41.

, "A Review of Automatic Theorem Proving" Mathematical Aspects of Computer

Science. Proc. Symposia in Applied Math, 19 (Providence: American Math. Society, 1967) 1-

7 8.

P. Suppes, Introduction to Logic (Princeton: D. Van Nostrand, 1957).

343

342

con PUT BBS

CLAY AND CALCULUS

Doiinic Soda, Aaron H. Konstan, and Judith Johnston
The Lindenwood Colleges
St. Charles, Sissouri 63301
Telephone: (314) 723-7152

Introduction

The beginning student of calculus has had very little experience in dealing with or using

functions of more than one real variable. One serious conseguence of this lack is that the

beginning student is often unable to associate the subject vith any reality, geometric or
otherwise.

The saie comments would apply to the one variable calculus were it not for two

circumstances. First, beginning students of calculus have had soie experience with functions of

one variable in high school. Second, alnost every situation studied in the subject can he
presented to the student by leans of a graphical representation. In this subject, the feeling
pervades that one can deal with "any" function. Given the function, one can find its regions of
increase and decrease, its naxina and minima, etc., and its Taylor expansion about any point;
indeed, one can even find its cartesian graph which serves as a reasonably coherent picture ot
all of these. This type of picture serves as a faithful if inperfect guide through the subject
and nany of its applications.

However, in the study of functions of lore than one variable, it appears that reliance on
graphs must necessarily be weakened at the outset. The difficulties encountered in drawing a
picture of the graph of a function of two variables are too well known to repeat here. A tine-
honored nathenatical principle is used to circunvent these difficulties, i.e., "reduce to the
previous case:" nanely, reduce the problen to a fanily of one variable probien by "sectioning"
the graph in various ways. Oltinately, all the infornation obtained by this process must be
synthesized into a coherent picture of the original. This last step nust be accoaplished
verbally and/or nentally because it cannot be carried out easily in a drawing.

In this paper, we shall describe sone efforts that we have nade to provide beginning
students with sone rich and interesting experiences with functions of two variables. These
experiences were designed to provide an opportunity for students to exanine and study many
functions of two variables directly, without the tools of calculus. Their study included
analyzing the function and then putting the separate pieces of infornation together into a
coherent whole.

Description of the Actual Experience

The students involved were, foe the most part, sophonores vith a year of calculus. The text
used was Lang's A Complete Course in Cajcu^as. The experiences described occurred while the
students were beginning the "Second Course," i*e«, the study of functions of several variables.

Following a brief study of the geonetry of fP and of curves in Kn , the study of fron
Kn*£ was begun. In nost cases n was taken to be 2 or 3.

Available to us were sone soft modeling clay, a clay cutter (a string of taut steel wire),
and a conputer progran (described below) which could produce five inch by five inch discrete
plots of the level curves of any function of two variables.

At first the clay was used to represent concretely ideas and operations that were formally
described. The class readily constructed and cut up various sinple surfaces, such as spheres,
cones and saddles, and observed what was happening. Generally there was great enthusiasts tor
this sort of activity. Several students becane quite adept at producing very interesting ruled
surfaces by taking a block of clay and cutting it on the wire.

One lecture on the level curves of a function of two variables was given and several
exercises were worked out "by hand." At this point the conputer progran aentioned above was
introduced briefly. Each student was given a copy of the "call progran," and those who
understood how to operate the conputer taught the others. The general project given was to
"investigate functions of two variables." In particular, each student (or, in nost cases, each
group of students) was asked to choose any "interesting" function, study it over any range, and
produce a clay nodel of the graph of the functions over the chosen region. For exanple, models
of the following functions were produced:

SSL. j eos(x,y)j x3 + y3 - 6xy

x3+y2

343

344

FIGURE 1 : Clay model of function z = + y3 - 6xy.

345

344

Students 'pent nany hours empirically examining functions using this technique. Computer
generated contour plots were used to inagine the graphs of the functions.

Immediately following this the class was asked to skip directly to the section of the text
which had problems on maxima and minima and to do every two variable problem given, empirically,
with the use of the computer.

Description o£ £h£ Computer Programs

in describing a program to be used by students whose familiarity with computers varies
widely, three principles should be borne in mind. First, the program must be simple to use. Any
information necessary for the operation of the computer program must be contained in a brief,
easy-to-read description of the program or, preferably, typed out by the machiue as it is
needed. Host students who are apprehensive of any device popularly labeled as a "thinking
machine" are reticent to absorb any large body of facts before executing a program.

Second, such a computer program should be as foolproof as it can be made. Ideally, no error
that a student could make in executing the program should result in the machine either stopping
or running on endlessly without indicating what error has been made. Likewise, the student
should not be confronted with the computer's waiting for some input without first indicating to
the student what kind of input is required.

If, in addition, the computer program is to serve as an efficient learning tool it must be
flexible in its operation. That is, it should operate in such a way as to enable a student to
"wander" through the relevant subject material in a manner which seems proper to him. If, in the
middle of exercising one capability of the program, the student becomes curious about some
related material, he should be able to abort the sequential execution of the program and
transfer to the part of the program which will allow him to satisfy his curiosity.

The programs described in this paper which work together as a unit were designed with the
above three principles in mind. Once the program system called EVALF has been executed, a
complete description of the capabilities of the programs and step-by-step instructions as to
what to do next are given to the student by way of the computers console typewriter. All the
programs in EVALF are written in F0RT8AN and run on an IBM 1130 computer. The student can
communicate with the computer both by typing on the keyboard and by using one of the fifteen
console switches available on the 1130. Only the function which is being evaluated and/or
plotted needs to be entered via the card reader.

The function Z ~ F(X,Y) is stored in the memory of the computer via the card reader as
FUNCTION Z(X,Y). Only one of these functions can be stored for active use.

Upon execution of the plotting routines of EVALF, the student is asked tc input values for
the upper and lover limits on X, Y, and Z. Then the student is asked to decide whether he wants
the large or small plot. The large plot is 30 lines down and 50 characters across with 11
contour lines, while the small plot is 17 lines down and 25 characters across with 6 contour
lines). The graph is then produced together with a key for the contour lines. In the small plot
the contour lines are drawn using the characters 1 through 6 ; on the large plot the characters 1
through 9 plus A and B are used (see Figures 2 and 3). It is then possible to replot the same
function using different limits or to enter a new function to be plotted.

In most cases the student using EVALF has little or no feeling for the range and domains in
which the function is interesting. Our system allows them to search for the regions of interest
using the small plot routines and then to use the more time-consuming large plot routines to
investigate these regions.

345

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It should be noted that whenever the plotting routines are used, the plotting procedure can
be aborted by use of a console switch. This allows the user either to correct nistyped data or,
upon seeing that no contour lines are being produced, to switch to another region of space
without having to wait for the graph to be conpleted.

Beactippq to the Experience

Before turning to our conclusions, it i
The students enjoyed this non-verbal, infornal
their own consents but also fron the fact
outside of class studying functions.

One student consented explicitly on the
calculus around her, i.e., to use the ideas
reality.

The experience also served to introduce i
conputer and to stinulate a desire to use it I

ight be useful to aention sone student reactions,
experience. This could be judged not only fron
that nany of the students spent considerabie tine

fact that for the first tine she began to see the
to interpret reality, particularly geonetric

everal students (and one of us) to the use of the
urther and understand it better.

Conclusion

The whole experience to which these students were exposed had four stages:

1. Obtaining and studying the contour diagrans of the function.

2. Constructing slab clay nodels of these contours.

3. Constructing the nodel of the graph fron the nodels of the contours.

4. Specifying the scale.

The total experience and the four stages described a^re analogous to one of the basic procedures
of coatenporary nathenatics. In fact, let f:X — * Y be a napping between sets; then the
following diagran is connutat ive:

natural

■>

l, R ^

inclusion

The fact that the diagran is coanutative siaply aeans that f is conpletely deterained by
"natural," T, and "inclusion." '

The ain of the experience was to help students develop their ability to visualize functions
depending on nore than one variable. So far, 25 students have had this experience and it appears
to have been successful. This conclusion is based on student reactions and on an infornal
comparison of these students with students who have not had this experience.

The students quickly developed the ability to iaagine what would happen if stages (2), (3)
and (4) were carried out. This leant that only stage (1) needs to be carried out explicitly. The

347

tedious aspects of this step are quickly and effectively done by the computer. The student is#
thereby, able to study many functions, or to study one function extensively. He can be given
challenging aulti variable non-linear probleas and can solve then efficiently. All of this can be
achieved prior to the introduction of abstract tools. In fact, this experience paves the way for
an effective initiation into the use of aore abstract sethods.

These computer produced contour plots becoae one of the nost useful and effective tools at
the students* disposal. They are used to solve practical probleas and to understand nev concepts
being studied; thereby becoming the bridge between these tvo activities. Perhaps this is the
optinai role for the computer in calculus (or in any other aathenaticai subject)* In this role
the conputer becones a versatile and effective vay to individualise the learning process.

The vide variety of clay nodeis that a class can produce in a fev hoars are useful visual
aids for lectures or discussions on the calculus of several variables.

These experiences could have vide application. They are accessible to anyone vho
understands or vants to understand shat the vord function neans. Calculus is not necessary in
order to carry out the experiences and solve practical probleas. Thus, they are available to
students vithout extensive mathematical background, for exanple, beginning science students? or
high school students. Indeed, the experience vould be useful to any student interested in
understanding quantities depending on nany variables — a vide audience, to say the least.

The usefulness of the nodeis has led us to try to produce soie clear plastic nodeis
corresponding to useful and interesting functions. Bovever, a nunber of technical probleas in
vorking vith plastic renain unresolved, We also investigated the possibility of using holograns
as a vehicle for representing the graphs of these functions in three dinensional space. Hovever,
the high cost of the aaster hologram (approximately $1400) prevented us froa implementing this
technique.

We are attenpting to use similar nethods in studying functions fron fc2 to t2 (or ? to ?)
but as yet have only begun this. Such prograas could make beginning linear algebra and
■ultivariable calculus nore videly accessible.

* * r
r f ir

349

APL AT HAflPSHIRB

Everette Hafner
Hampshire College

Amherst, Massachusetts 01002

Su&fi&£Z

Nov in its second year of experience vitb students working in a new curricular framework,
Haapsbire College has devoted a large effort to drawing its people into coaputer consciousness,
with APL as the language of aain interest* The principal facility for the project is UHASS, a
tine-sharing systen based on a CDC-3800 installation at the University of Massachusetts at
Amherst. Points of emphasis in our approach are: (1) the use of video tapes and other aids to
self-instruction in computer technique, (2) encouragement of independent study through the
invention of original programs, (3) applications to the arts, (4) experimentation in
mathematics, and (5) simulation of physical phenomena as a complement to laboratory work. This
paper presents typical results of the effort so far, with enphasis on examples generated by the
author and his students.

He are told of a ausic professor, new to computer languages, who encountered great
difficulty in writing a BASIC program for producing an unending sequence of twelve-tone rows. {A
tone row is an ordering of the twelve notes without repetition.) He took his problem to a
colleague in physics, who happened to be working with APL at a computer terminal, tfhile he was
talking, the physicist casually typed a few lines, tore off the page, and asked the composer to
repeat the problem slowly and clearly.

Then he said# "Hell, George, this terminal is equipped with a microphone. It tries to
understand easy problems and work them out for us. fours is easy enough. Try typing in the word
TONEBOW and see what happens.1* After a little more encouragement, George tried it:

and so on, until they stopped the program.[1]

Whether it really happened or not, the case illustrates some things about APL that are of
first importance to us: its fast access to computation, its mathematical elegance, the good
sense of its built in format, its concise structure, and the mnemonic aspects of its character
set. This is not to say that the language does not have some clear disadvantages in comparison
with, say, PORTRAN. There may be little doubt that for most conventional research problems, with
large stores of data and highly iterative procedures, APL is not ideal. But it seems to us to be
the most deeply rewarding approach to the computer for people whose aim is toward understanding
the nature of the computing process itself. One purpose of this paper is to suggest, by example,
the several ways in which APL has worked well for us. Another is to invite comment and criticism
from groups whose experience may have been different from ours.

A principal challenge of tha Hampshire program is the development of useful tools for
independent study, especially on the part of students whose preparation and incentive are
initially weak. The computer can enter this picture in a variety of ways, many of which
(especially the notion of computer-programmed stepwise instruction) have been explored at
length. We have a new idea about this. Take a student who is naive in science, yet curious
about the ways in which scientists operate. Give him a brief course (we use a set of brief
video tapes) on the housekeeping aspects of an APL terminal. But tell him nothing of the
language except a few points of convention: how to create variables and arrays. Urge him to
imagine an unexplored world of "laws9* to which the terminal gives us access. It is his world to
study with whatever ingenuity he can muster; it is then, in a tiny sense, a model of the real
world.

Host people in this situation fork quickly through the easy APL functions and begin to
understand how the language is organized. Before long, their experiments develop a scientific
flavor. There is indeed a good strategy for investigating an APL function just as there is for

T0NER3W

6 1 1 10 7 2 4 3 12 8 9 1 5
9 1 12 1 1 7 5 8 3 10 6 4 2
6 11 9 2 3 12 7 10 1 5 4 8
5 1 1 7 3 10 6 8 4 9 12 1 2
12 1 8 2 3 9 7 5 6 10 4 11
11 1 S 3 8 4 9 2 10 7 6 12
4 10 9 3 7 6 8 2 11 5 1 12
8 2 6 7 3 4 5 10 12 1 9 1 1

ERIC

349

350

finding lavs of nature. It is to some extent the same strategy: sake a hypothesis, design a

good experiment, take data, test the hypothesis, and go back if need be.

The model is a good one in some respects that are not obvious. For example, the first
experiments with in APL tend to be puzzling:

: 1

?\ 3 0 mo 1000
3 C 4 £ r> 3 3

n 2 t r

'jor;::: rrpoj

??. 5

?20

It appears already that the domain consists of the positive integers, but our attempts to
associate a function with "?" are never successful. The idea that it may not be a function does
not arise easily; it takes most people a long time to try the same argument more than once:

?1 2p1 00

100 37 25 99 73 76 66 8 64 89 28 44

As soon as one sees results like this, he begins to see the role of "?" as a random number
generator. Learning its properties from then on is easy. The parallel with experience in science
is clear and interesting: a habit of thought can be an obstacle to progress.

Our next remark has to do with APL as a tool for the study of mathematics. A student asked
to investigate the primes typically begins as follows:

vppirrs rn]v

V V.+PPTri'r LT:'T?\

r i ] t:<-o xr ;>-i + ? x \ 7.1 ::i?

[2] +( 0s*[W+! ] )/?

I 3 1 -(n = .'<-| (7,.r;rf7?-cf)^Mr«n)/5

[ ] -*■? , o £IV+.'*fV] x i r ]«-n

r r>] '/.<-? , ( ;<>n )/?.

VSIM'S 2 0

2 3 h 7 li 13 17 39 23 20 31 37 41

Mis next step might be to look at the distribution of primes in graphical form:

r+rrz-rr 7 rcc

4 o o 1

.;,f son

C OCp '

/?[/’ r » 5S0]]«-'fM

r o sof.r

r'..l !! [; - n (-; [i rj

n f! r.; ri n n
l; u n r; u

l: c [] r;

n [•

ij (! r: ri □

v [' f ' n

n o nun u

n o rj o

n n [ c n

rs n nn on

n u ri n n

rj ri u n

u n n r.i

351

where ve have reproduced the first few lines of the long array.

The algorithm used here is conventional, but let us now introduce a new viewpoint. Suppose
we ask the student to write an API function for prines up to N in a way which expresses the
mathematical definition of prine nost directly. The function should simply choose the set of
integers such that each is divisible only by itself and 1. A response to this challenge is:

VVEATMinr A1

Cl ] (? = + /n ]o = ( 1.7)0. 1 1//)/ 1 ;;v

UEATPPHir 5 0

2 3 5 7 11 13 17 19 ?3 29 31 37 Ml 43 47

This function is our favorite exaspie of the power and conciseness of API. It also illustrates

extremely well the close correspondence between the structure of the language and sathesatics

itself.

The last observation has led us to look at sose ways in which a student can lead hisself

through a branch of sathesatics. There are the usual obvious things to do in nusber theory. But

what about nodern algebra, for exaspie? ve have constructed a heuristic exercise on a nine-
element field which lists the addition and nulti plication tables and verifies the nine field
postulates by testing all possible cases. The whole process is fast and sinple in A PL. Here, for
exaspie, are the tests of the two associative lavs:

a/a/a/((;/ a X) A X)=X A {X A X)

a/a/a/((X .V X) ,'f X)-X M { X fl X)

where A and H are functions for addition and nultiplication over all elenents of the field X.
The exercise continues with a proof of the quadratic fornula, after discovering that there are
only 45 (out of a possible 72) solvable quadratic forns in the field. Ve prove the fornula*
easily by shoving that it generates all possible pairs of roots. The student is left with a
final thought: "It night be interesting to suggest that theorens which are proved on a finite

field can serve as conjectures to be investigated on other fields, even including the field of
real numbers. ”

The problem in algebra, carried out entirely by conputation, is entirely free of fornal
proof. It tends for this reason to raise eyebrows, and even to sound alarns, anong
mat henaticians (including students in love with the abstract). But ve find the idea powerful and
vivid: it can give an illuminating first view of a aathenatical structure, perhaps as
preliminary to a more fornal study. Another possibility is that, through conjecture and test, it
can produce new knowledge.

our best example of actual mathematical discovery cane about in an exercise on reciprocals
of primes. It is well known and easy to prove that if p is a prine whose reciprocal has period
P'1, then the first p-1 multiples of the corresponding integer permute cyclically. For instance:

0.1-2 a 571420

6 Ip 142357* 16
142857
235714
423571
571422
714285
857142

The set of prines with this property is 7 17 19 23 29 47 59 ...

search for reciprocals of appropriate period. Ve wrote a function
reciproca is :

* V Z+P PKC DiQiXiS

[1] Oi~l+/N*l
[ 2 ]

C3] /?«•(/?*£? )-S*P

[4] +2M (P-1 )>pZ+Q

and is usually found by
for arbitrarily large

ERIC

351

7 RKC 10

1 4 2 0 5 7

and found, for instance, that the reciprocal of 61 produces the 60-digit nenber

0 1639 3442622 9 S081 96 72 131 147540983606557377049180327868852459

whose first 60 nultiples are necessarily cyclic. The APL function forced upon us an awareness of
base 10 in computation, and led us to a crucial question. Does the cyclic property of a prise
depend on the number base? Suddenly one realizes that the reciprocal of 2 expressed \u any odd
base is a trivial case, and a few trials with other primes quietly raise the conjecture that for
every prise there is an appropriate base. A few more steps, and a little somber theory, produce
the central theorem for this problem:

The reciprocal of any prime p expressed in base b is cyclic if and only if b is a
prinitive root of p.

(A prinitive root of p is a number whose (p-l)st power is the smallest congruent to 1 modulo p.)
The problem has been solved.

Me cone next to a conjecture in statistics. Consider

r::

,€)?( //.«■♦/( I 2 3)0 . =L n .*+(♦/?( :'V')p?l ) * •*) \ 1

0 0 1 0 7 6 13 15 19 24 1 9 10 20 14 7 3 2 1 1 0 0

n fj
rn\ n
pl'G r:
no: n
maun
nnnnrn
[innnrnn
nnriimc

Lfriiiaitincj
( UGL'tO-lD
Uifipc-rnri

r-unririrnn
Li nnnntinnnn
mvrnuvn

PPPUEiPLlLIlGL)
cnuEJijnLmnLi
nMinrnrnnp
Ltirjnfupnnrnnn
n nnRnrjanGnunGCTJtJ

This beautifully concise function computes H rounded means of H random integers from 1 to 21 and
plots their histogram. (The example is typical for samples of means of 4 integers in the
domain.) One observes that the distribution has central tendency at 10, and grows sharper with
increasing H. tfe suggest to the student that the frequencies are distributed normally. He
studies the trend of variance with H and attempts to justify it in a formal way.

tfe like to raise questions suggested by the history of computation. In 1914, Ramanujan
discovered that the rational number 2143/22 approximates the fourth power of pi to about one
part in three billion. It is natural to ash how lonely this number is in the class of fractions
running through the integers to 10,000 and approximating any of the first four powers of pi.

3^3 352

Hence

V :: SEARCH .V; .T

Cl] ?.T-Ol

[2] /-I

[3] «/-l

['»] w^iri jiPi*i

C5] -<</?> 3, li. 1502 )a( (/>( ) <3. 1415 93 ))/S/'0.'/

C 6 ] •» ( ( +1 )=/. + 1 ) / 5

£73 +UUJ+J+ l)/4

[8] -*(;-/aif/+i )/3

[9] -*-0

[10] SilO;/: + ((J r,CD ;.')*1)/G

[11] T+(JiK)*iI

[12] J,<{,J,r,(10*"2)xL0.5 + ( 10*10 )*T-P1

[13] -»G

V 5T.0 ,v

[ i ] z*-//

[ 2 ] :>:/ 1 //

[3] //*-Z

[4] -*0*..'

4 SEARCH

1 0000

355

113

3.141592921

26 .69

OfiOl

319

3.141592418

"23.52

2143

3 . 141592653

"0.09

where the first two colnnns reveal the integer pairs, the third gives the power of pi
approximated by the fraction, and the fifth is the error in the eighth decinai place. We see
that there are only three cases in which the error is less than about 50, and that Rananulan's
nun her is best by a large nargin. Dil he actually perforn a search like this (without a fast
conputer) or was he sinply lucky?

We give two exanples of our approach to con puter-assisted instruction. It is our view that
the nost efficient node is sinply a brief test of one's ability to carry oat a task. Here is a
program on orders of magnitude:

ri] 'rstie'/tf the po:,lc::i::g products , to the erases? higher'

[2] 'Op. LG TER PCK.’EP 0* 1C. TYPE t. he appropriate EXPONENT . '

[3] 'POP. APPLE, IP THE VALUE IS ABOUT 250 , EITHER 2 OR 3'

[4] '15 ACCEPTED. YOU CAVE 15 SECONDS.'

[5] C-l+R+t)

[6] delay 2c

[7 ] PR 2 : '/,*■(. ?5pl00)x10*_4 + ?5p5

[8] ' PEOPLE: I ' ; C

[9] SCl];'*';Zr2];'x(';Z[33;'*.5)x('j2[4];»*2) 4 • ; 2[ 5 ]

[10] Z*10»ZCl]x2r.2]x(:;[3]*0.5)x(Z[4]*2)iZ[5]

[11] T*- 120

[12] A+r.

[13] 51. xi(I20)>1"+2500

[14] Z),(A>[Z))/SV,LG

[15]

' YES . '

[10]

/?«-/?+ i

ri7]

+''PLP

r a p]

<7;Vf • »

S'1 ALL .

VALUE

TE A ROUT 10*'

;( ri0xZ)5i0

[19]

CP HP

[20]

LG ; * TOO

LARGE.

VALUE

IS ABOUT 10*'

;( r 10*Z)*10

[21]

C PLP

[22]

CL: '700

5 LOR. <

[2 3] :!PLP : X x ruc->-C+ 1

[24] ’YOUR SCORE IS OUT OF ' j L 1 00x Pi U ; ' PERCENT '

353

PPODDE! 7 5

est r/.'/i tf the follopiug products, to ?pe heapest pigiiee
or lopee dopm nr to. type the apppoppiate expoueht.
fop uxauple, if the valve is about 250, either 7 on 3

IS ACCEPTED. YOU I'AVE 15 SECOHSS.

PEOPLE!! 1

li.2*5|l0*(‘*.7*.5)*(290*2) ! 0.10

r-> '

yi:s .

*J nOHI'EX ’ 7

0 . 09x9 . 6x ( 750* . 5 ) * ( 0 . 056* 2 ) + 9

too lAnn '//,/ii/E /s / /? n t/ r 10*“?. 3

and so on.

The second test criticizes one*s atteapts to rearrange and solve a linear equation,
prograa sets up at randoa. The APL function yields 1 for every true relation in X
identities), and 0 for everything false:

I'tJV'Q D

want instructions? type y op .v.

( ( 2*X) + ( 7 + 3*A') ) = ( + ,Y+“3x*t “3 )

((4x*)+7) = (X-l)

X - + 8*3

*=-8*3

2 . G66666667
TUTOR

i WANT INSTRUCTIONS? TYPE
N

Y OR A* ,

( X'fX * 2 ) = (XtX)
* = o

TUTOR

WANT INSTRUCTIONS? TYPE Y OR N .

(l+(“lx*)+(“l+~2**)*~5) = (“3+(8x*)+(5+9x;Ot“5)

( (“3*X*s>+&rS> = ( ( 31*d*5

XtS) -4)

X = 1 7 i 1 3
X = 13*17

355

which the
{including

354

(The program for this exercise

is available on request.)

We have built a library of interesting mathematical sequences, mainly for the purpose of
studying their rates of convergence. Here is a familiar seguence converging to the square root
of any positive number:

►( ( ! ([*♦

- o . r. x y + v ; v )

)>10*“l5 )/l

1 . ‘I 7

1 . 2
i .4:4?

: . ui i, 2

)

The accuracy doubles at each step.

We have encountered soie excellent examples of conjecture and experiment in geometry.

Typical results:

One of the best has led us to the theorem
illustrated here: the midpoints of the three

chords joining arbitrarily chosen 60-degree arcs
of a circle are vertices of an equilateral

triangle. Before attempting proof, which is
straightforward but arduous, we composed an APL
function which returns, to 14 significant figures,
the lengths of the three segments determined by a
pair of angles, in radians, arbitrarily chosen for
each test.

TRI 1 2

1.3593192074603

TRI 1 3

0.94802829331059

0. 94802829331059

0.94802829331059

TRI 2 3

0.60594333139318

0. 60594333139318

0.60594333139318

TRI 3 3

0. 12721726366189

quickly bolstered our confidence in the truth of the conjecture.

We have been using APL with good success in simulation of physical phenomena. The following
function, composed for a course in acoustics, yields the progress of longitudinal waves on a
lattice of identical masses and springs:

355 ;> ,

r 1 j ;v(i+:,^r:| l])o> 0

[Pi

r m ^s/>(:d»y) + ("i<»,)-?»if
rwi :n ]<->:[ ;■ + !>'

[ r. ] y«- :'+/>? *i'«-r+;: x ( ?r<-r [ ?] )*:’*( >:-3 )* ?s

r g j *(~v/(r*ro:,j=,>o. r>* iff 2:1*0. s )/avfa?

r ?,] ^

[ G ] *»60

[ 9] //'/,Y«V :*♦(<?[ 2 ]>r)/r?f)

r i oi ,■<-$( ( ( py) t m+ i ) ,.”+i ;d.m
nj v«-o , I o. 6 + i oox.v
[12] ^((/.,+ 2)f((p:-,)4/.,+ 2))p//

P/A VK 15 10 .1

, 5 1

. 5 0

0 0

r>0

100

.50

0.5

1; i

~4 7

“27

“4

1 . Si

"24

"4 3

“32

"lC

4 7

“1?

”40

" 3 C

“29

2.0

“a

“33

“ 3 7

“ 3 C

" 1 2

4 2

“l o

1 0

"23

"35

‘39

“27

3. Si

‘10

"12

~ 3 0

“ 3 9

"38

“a

“4

1 4

“ 7

“23

"35

‘4 5

“17

4. Si

“4

"10

“15

"29

“47

“34

1 8

“l

‘6

“l 3

“a

“25

“54

“67

“43

Si . 5

“l

“7

“l 5

“15

“42

“71

‘GO,

“l

‘2

“7

“2 3

"2 5

"24

“a

C. Si

“l

“11

“18

‘15

“42

“32

2 4

5 6

“l

‘2

‘1

”l'

“ 1 4

“32

"38

. 3 a

1 7

7. 5

“2

“l

“7

“14

“21

"37

“20

r»

“15

”0

" 7

“3

“10

“iG

"28

“32

“l 0

1 5

“3

“l

“10

0 . 5

‘13

“21

“31

“25

5 0

“l

‘4

‘lft

“l 3

‘24

"31

"l 7

4 4 1

4 9

“15

“10

9. 5

***17

“22

“4

2 0

“ll

“15

“12

1 0

4 5

“4

“l G

“5

“14

In the example# a deformation at the left end of a 15-element system returns vith opposite sign
(and soie distortion) after reflection fron a fixed end. On the corresponding continuous system#
reflection would occur in 10 units of tine.

looting to the uses of computers in the arts, we have worked vith APL as a tool for
coaposition of music# as veil as for study of oroblens in nusical acoustics. It has been
interesting# for exanple# to conpose a set of functions for exanining divisions of the octave in
equal tenperaaent. We then carried out a search for tenpered scales which contain acceptable
diatonic intervals. If one gives high weight to perfect fourths and fifths# the first few good
scales have divisions of 12# 17# 19 and 22. If we include the two musical thirds &s well# the
sequence begins vith 19 and 31. The 19-tone scale is especially attractive for the perfection of
its ninor third# which it produces vif h an accuracy of 0.01 per cent. We have therefore learned
to set the keyboard of an electronic synthesizer for performance of nusic written for this
scale.

The principal conclusion fros our experience so far is that APL lends itself vith good
effect to an extraordinary variety of tasks and challenges. It has therefore been a major
contributor to the development of programs in a new experimental college.

There is# however# a large unanswered guestion which we set before ourselves is early
stages of science planning at Hampshire. To what extent can vise use of the computer make it
possible ^or a student of science to avoid# or at least to delay# a major investment in the
formal study of applied mathematics? We expressed an early hope for this in the following way :

"It was once necessary for students of any quantitativ e science to acquire
fundamental knowledge of the group of mathematical discplines (mainly in
analysis, ordinary and partial differential equations, probability, and theory
of functions) whose applications form the body of theoretical science. But we
are now in a position to persuade our students that modern computer science
exposes much of applied mathematics as a set of programmable procedures whose
theoretical foundations can be left to specialists. Indeed, it has become
increasingly clear that a computer-based approach to applied mathematics is
moffe versatile in application than the approach through pure mathematics.
Students of limited mathematical talent need no longer confine themselves to
the simplest, analytically nost manageable (and often least interesting)
examples of a scientific problem. The computer i^ their servant in displaying
wide variety of example within a simple mathematical for malism. N[2)

The statement is perhaps too optimistic. Re think not. But more important is the question of the
philosophy itself. Some scientists (especially mathematicians) react with horror to the idea.
Others see it as at least worthy of exploration. Re take the view that the pedagogical
feasibility of fast and elegant computation is far from known, and that institutions like
Hampshire must devote part of their effort to the question.

The author takes pleasure in acknowledging the assistance of many colleagues, including
especially Kenneth Hoffman, Kenneth Iverson, Howard Peele, Michael Obeli, Rebecca Wills, Conrad
Wogrin and John Wright. Computer facilities at the University of Massachusetts, SUNY at
Binghamton, and the IBM laboratory at Poughkeepsie were essential to our project. Pinanciai
support for part of our work was provided under a grant from the Esso Education Foundation.

11] 12712

[2] IV

2. E.M. Hafner, Arches of Knowledge , Hampshire College Planning Bulletin 10, August 1969.

REFERENCES

1. What the physicist had typed in was simply

VTONBROW

COMPUTER GENERATED PICTURES FOR TEACHING CALCULUS

Roger B. Kirchner
Carleton College
Northfield, Minnesota 55057
Telephone: (507) 645-4431

In a paper given
instruction which could
classified as investig
useful. In this paper,
output of programs of t

at the Iowa Conference! 1 ]# the author presented programs
be run fro® an ordinary tine-sharing terninal. The
ative, instructive, and illustrative. This classification
we enphasize the use of 35 on slides that can be taken of
hese three types.

for oia theita tics
prograns were
continues to be
the graphical

The computer system used consists of
teletype for input-output, and a KV8/L graphic d
Oscilloscope. Since the storage scope is suitabl
at a tine, it was decided that the best way t
graphical output was by means of 35 am slides,
motivate students to use the instructional progr
ordinary and con puter-orien ted sections of calcu
Sequences of slides can simulate the experience
storage scope, and they can improve the direct e
is needed to generate each picture.

a PDP-8/L computer with 8K of nenory, an ASR-JJ
isplay system with a Tektronix 611 Storage
e for viewing by only a snail number of students
o communicate the results of programs with
Initially, the main purpose of the slides was to
ans. However, in showing the slides to both
lus, they were found to be useful by themselves,
of viewing the generation of pictures on a
xperience in cases where more than a few seconds

It does not seem to be critical that the student sees the pictures being generated on a
scope. It i £ sufficient for him to know that he could duplicate the pictures if he had access to
a terminal with a scope. Although the student loses the freedom to vary parameters when he can
only see the slides, this is less of a disadvantage if there is a rich variety of slides avail-
able. It is thus hoped that, by duplication, the slides produced can be of use to instructors in
schools where graphics capabilities are not available.

In ves t iga five prograns allow a student to study a class of procedures such as root finding
methods, or a class of mathematical objects such as rational functions or implicitly defined
curves. A specific example is TAYLOR, in which the user has the option of studying Taylor
polynomials for any of nine different functions. With some, he can specify the point about which
the expansion is made. He can specify the domain, the range (scale equal to the domain scale,
specified maximum, or computed maximum), and the polynomials he wants to plot. The computer then
sketches the function and the approximating polynomials. Photographs T-1 through T-5 show some
approximations to sin x near x - .2. One observes that the 2k-1st and 2kth approximations are
very much alike. But the approximations are polynomials. Consider T-4. Can an 8th degree
polynomial look like a seventh degree polynomial? The user will want to sketch another picture
of these polynomials using a larger range and domain.

Instructi ve programs are designed to introduce and reinforce a mathematical idea such as
the limit concept, the definite integral, or the fundamental theorem of calculus. Pictures have
been included from three instructive programs, YOUEP ("You Epsilon He Delta"), HEEP ("He Epsilon
You Delta"), and PNDTHH •

YOUEP and WEEP are games originally programmed to run at a teletype, and were described in
the Iowa paper. Playing them on the scope is much faster, and they are much more instructive
when a graph of the function being studied is sketched. First the rules are stated. Then, f(x),
xQ, and L are chosen by the user. The computer makes a judgment about its chances of winning, in
YOUEP, if the computer thinks it can win, it will use an estimate for a Lipschitz constant at xQ
to produce a delta tor any inputed value of epsilon. If it thinks it will lose (the estimate tor
a Lipschitz constant is large), it will resignedly try three successively smaller values of
delta for each inputed epsilon, and thus force the user to play carefully. Photographs Y- 1
through Y-14 show a sample game of YOUEP. f (x) = xsin(1/*)# xQ. - 0, and L ® 0. The limit is L,
and the computer senses this. When a value of e is inputed, the computer sketches the graph of f
near x0, draws a horizontal strip of width 2e centered at y = L, chooses a value for 6 (in this
case 3' - .9007196 which is clearly small enough) , draws a vertical strip of widtl* 25 centered at
Xq# and waits for the user to input a value of x. The result of the users response is graphed,
and the relevant calculations are made. In this example, the computer eventually wins.

Part of a short game of HEEP is shown in photographs PI- 1 through n-3. Here the roles of the
players is reversed. Note that the computer has found a winning choice for £.. The games are
actually a little more fun to play when the user can win. Then the user can play a little
sloppily and test whether the computer can take advantage of his mistakes, k significant feature
of these games is that the user does not have to think about scaling. That is done
automatically, and he can concentrate on the ideas. It may be useful to modify the programs so
that the point of the games is to find winning formulas for c, 5, or x. They would then have an
investigative rather than an instructive flavor.

359

T-1

Y-U

Y-5

Y-9

Y-11

363 '

36'1

364

M-1

M-2

F-1

F-2

F-7

367

PNDTHfl is a program designed to verify the fundamental theorea of calculus. The user
chooses one of ten functions* an interval [a*b]* and a positive integer n. On the upper half of
the scope* the computer sketches the graph of f on [a*b]. On the lover half* it sketches the
graph of P(x) - P(a)* where F is an antiderivative of f. Then* for i from 1 to n* it draws
rectangles which define lower and upper subs for f on [.a,X£] and plots values of these suis on
the lower graph* where X^ ■ a ♦ (b-a) i/n. The graphs of tlie lover and upper sums are aade
piecewise linear. Pictures F- 1 and F-3 which attempt to explain the situation are unsuccessful
because the description is not quite accurate and there is too much information on each picture.
The programmer was too involved in getting the computer to draw sigmas and integrals. However*
one can see from the definition of FEIN (I) and PHAX(I) in P-3* that the sums are lover and upper
suns only when the local extrema of f are subdivision points. Some simplification like this was
unavoidable.

The development of the graphs is quite interesting to watch. It is almost movie-like. One
observes that F(xi) - P(a) is always between the lower and upper sums for f on [a*xi]* and is
led to the conclusion that a/xf(t)dt a P(x) - F(a). See pictures P-5 and P-7.

I j lust rat ive programs demonstrate unusual examples or counter-exaa pies. Examples are the
graphs of ~approxi mation s to the Cantor function* to a non-di f f erent iab le function* and to a
space filling curve. Unfortunately* because of limited access to enlarging and printing
facilities* no prints of these pictures are available for this paper.

The photographs were taken with a SLB camera using Kodak High Contrast Copy filn (ASA 64)
and an exposure of 5 seconds at f5.6. The slides are thus black and white and project black on a
white background.

1. MPrograas for Computer Extended Instruction in Hathemat ics* " Proceedings of a Con ference on
the Computer in the Undergraduate Curricula (Iowa City: Universit y~of Iowa * 1 970)* pp. 4.37-
4.44.

REFERENCES

368

COMPUTER-BASED EDUCATION LESSONS FOR UNDERGRADUATE tfUANTUH MECHANICS

Carol Dm Bennett
University of Illinois
Urbana, Illinois 61801
Telephone; (2l7) 333-6212

Simulations using a computer to plot quantum-mechan ical wave functions for a choren

potential have been popular in physics education. They give the student the opportunity to
expedient with the behavior of wave functions without the distraction of complicated

calculations. Such simulations have been expanded and lessons written on the PLATO systen at the
University of Illinois. Brief descriptions of new lessons are given as well as how these and
others have been integrated into undergraduate physics courses. A new lesson on the two-electron
helium atom and a self-consistent calculation of the lo*est-energy electron wave function iu
described in more detail.

Science and engineering students work out the infinite square-well problei in detail in the
third-semester elementary physics course. A computer simulation is then used as part of a

lecture demonstration to show the behavior of quantum-mechanical wave functions for a finite

well. As the well is made deeper, they are able to identify the solutions for the infinite well.
As the well becomes shallower, more of the wave function is seen to creep into the classically-
forbidden regions.

As part of this lecture demonstration, using an on-line computer graphics facility, the
students suggest energy values in the search for the bound state solutions. Before they are able
to solve finite-well problems analytically, they get a feeling for the boundary conditions that
must be satisfied. This is usually a one-shot event at the elementary physics level and the
students* response is highly enthusiastic. Interest is stimulated in how the equations are
integrated numerically and how the bound state energies could be found analytically.

The next quantum mechanics course, for juniors and seniors, uses the computer lessons as an
integrated part of the course. Towards the beginning, the students individually work through a
lesson on phase and group velocity. The main features of this lesson are two "labs", one on
phase velocity and one on group velocity, in which the students can vary wave numbers and
angular frequencies to see a single wave or sum of two waves plotted at consecutive time
intervals. Before entering the first "lab" on phase velocity, the student is guided through
questions and exercises on the concepts of wave number and wavelength. At one point a sine wave
with a randomly chosen wavelength is plotted along a marked scale. The student is asked for the

wavelength and wave number, and must get three correct in a row to proceed. After each "lab" a

quiz tests the student's understanding of the relationships between quantities involved in the
phase or group velocity of a wave and the general shape of the wave. Key words in the questions
such as "increasing" or "decreasing" (e.g., "Increasing k has what effect on phase velocity?")
are chosen randomly because the student may have to repeat the quiz after additional
experimenting in one of the "labs."

Two later sessions with the computer are direclty connected with homework assignments. Some
of the problems are listed in the Appendix and could be used with any computer lesson that

allows a variety of potentials to be specified by the student. Such guided exercises greatly

add to the educational value of these lessons* One set of problems deals with potential wells
and bound-state solutions, and the other set concentrates on barrier transmission problems. A
favorite problem is the analogy with the optical case of a nonref lect ive coating. Until they see
the wave function plotted for the conditions they calculate, some students do not believe that
there can be 1 0 0 X transmission when the incident wave must pass over a change in potential.

Students typically work in pairs at the terminal on these homework problems. The interaction

between students during these sessions promotes added awareness of wnat is happening and

increases the amount of investigation into finer details of the problems. They ask each other
questions and then work together with the computer to find the answers.

Not all of the potentials studied using the computer are symmetric. For this reason, the
lesson that plots wave functions for square and asymmetric wells starts integrating from the far
ieft with zero amplitude and a slight slope, and integrates to the right. When the amplitude at
tue far right becomes very small, a bound state can be identified. The barrier transmission
lesson also integrates starting at the left and plots the incident plane wave, the reflected
wave, and the transmitted wave. The sum of these is then plotted to show that the total wave
function matches properly at the boundaries. Ft t the elementary students, however, a more
general lesson is used that leaves the starting point of the integration up to the user.
Building the symmetry of the square well into the wave function by starting at the center of the
well uith a positive amplitude and zero slope for symmetric solutions and zero amplitude and

positive slope for antisymmetric solutions is 2ess confusing for the elementary students.

An additional lesson was written for students to use before they start the lessons that
plot wave functions, it introduces them to the types of functions that are plotted in various

369

regions of the potentials and how amplitudes and slopes are matched at the boundaries. A single
step potential is chosen with random values for the left and right potential levels- For a
randomly chosen energy level, which could be either above or below the right side of the
potential step, the student is asked to give the analytic forms of the wave function at the left
and right- For ease in typing, the student uses "a", ubn § "c" and "dM to represent the general
functions "Ae^^x" , , ,,Ce“Kx“ , and "De^x" respectively- For example, when the student
types "a*b", the computer writes " + Be“ikx" for him, and then proceeds to give a response
appropriate to the answer- After calculating the wave numbers tor the left and right regions,
the student must attempt to satisfy the boundary conditions. When he has solved the equations
and entered values for the real and imaginary parts of the coefficients, the computer plots the
wave function to show what it looks like at the boundary- The student has an immediate check on
nis calculations and can see what to adjust if the amplitudes and slopes do not match at the
boundary. This exercise gives the student visual assistance on solving this type of problem that
he would not get on a typical homework assignment.

A recently developed lesson attempts to make the two-electron helium atom a possible area
of study for undergraduate physics students- The goal for the student in this lesson is to find
the ground-state wave function of one of the two electrons- This lesson has two major parts- In
the first part, the student identifies the forces involved, derives an expression for the
Coulomb potential using elementary electrostatics, then worxs through a simple analytic example
of finding the Coulomb potential for a given spherically symmetric charge distribution- In the
second part, th' student is to find numerically a self-consistent ground-state wave function for
the helium atom. THe self-consistent calculation will be described in detail-

Below is the "index" page that the student keeps returning to during the numerical
calculations. It shows the equations previously derived that must oe solved, and gives a
solution scheme with 6 basic steps describing a self-consistent numerical calculation- Many
students never see such a calculation in their courses although the methods are often used in
physics research-

a ) [(-t2/2m)V2 + Uc(r)]«S(r) = Erf(r)

b) Uc(r) = Ze2/r + Ue_e(r)

C) 72Ue_e(r) = -4ne2 [gS (r) \ 2 .

Solution scheme:

guess s^(r)

solve (c) for ue_e(r)

substitute U (r) into

e-e

(b)

find E and rf(r) from (a)

Compare ^(r) in (a) with

initial

iterate until tf(r) is consistent

Choose a step (1-6) :

Equation (a) is Schrodinger ' s Equation with the Coulomb potential Uc(r)>; equation (b) gives
r;c(r) in terms of tne potential of an electron in the field of Z = 2 protons and the electron-
electron potential Ue_e(r); equation (c> gives bTe-e(r) in terms of the electron wave function
£(r). The student can attempt to solve these equations for /0(r) starting with any of the six
steps, but he is told if his choice is inappropriate- For example, if he chooses step 4 before

having done anything else, he receives the message, " but I don't know tre Hamiltonian yet. I

need Uc(r) -,! Similar messayes are given for other steps when enough information is not available
to complete the step- The steps are detailed below- what appears on the student's terminal is
boxed in- Quantities underlined indicate what the student types.

^(r) will be assumed to be zero
past some maximum r=r

max.

Choose r : 2 Anqstroms

max 3

The student enters a number dc max. If the Lumber is larger than 5, he is told that a smaller
numner would be more realistic- The initial guess to the wave function is then entered as a
series of step functions- An example is. shown below-

! -\ <i

Guess i (r ) .

i (r) is to be ~ntereJ numerically in
step functions between r=0 and r=rm. x.

i (r ) =0, r >
0 . * r < .5 ,

. 5 < r < 1.0 ,

1 . 0< r < 1.5 ,

1 . 5< rr 2.0 ,

2.000 Angstroms.
JZ*(r) L:

**(r) " -d

• r > . 3

*U) = -1

The initial yuess the student gives is plotted and normalized for him. The normalized values are
available at any time later in the calculations by returning to the "index*1 page and reguestiny
step 1.

Step

2; For each interval, give the numerical

coefficients of the r^ and l/r terms in
•Ue-e(r). Press DATA for a calculator,

LAB for r and jrf(r). e^=14.4 eV-A.

Press HELP to review the sample exercise?
you can press ANS to fill in answers this
t ime .

1. 500 < r * 2.000 , jrf(r) = .050262
Ue_e (r ) = r-1 (13.18095 )

+ r2 (-.07619 )

+ constant (= .91429 )

DATA, LAB, HELP, ANS refer to special keys on the sfcudent#s keyset* Only one of the intervals is
shown filled in here. The student must calculate the numbers for all intervals starting from
larger r and working to r = 0* This is considerably simplified by being able t refer to the
sample exercise for a spherical charge distribution worked out earlier in the first part of the
lesson* A calculation mode s also available to the student*

Step 3:

Accumulate the total Coulomb potential energy
U . Give U (r) as a function of r for each
interval. Note: Z=2, e =14.4 eV-A.

1.500 < r * 2.000 , frf(r) = .050262
Ug_^(r) = ( 13 . 18095 ) /r + (-.07619)r2 + (.91429)
Uc'r) = r-1 (13.18095-28.8 )

+ r2 (-.07619 ) + (.91429 )

This step is straight copying froir. step 2 except for the 1/r tera which oust now include -Z$2 in
the coefficient. In this case, the computer was left to do a subtraction before judging the
answer as correct. The student is told whenever any of the answers are incorrect. When all
numbers have been correctly calculated, Uc and .’Ue-e are plotted from r - 0 to r = 1.3rmax-

She* 4:

The potential at the midpoint of 20 equal
steps between 0< 3.000 A is tabulated below.

These numbers are used to find the new

-364.

. 39

-9.19

-108.

.73

12)

-8.37

-58.

.21

13)

-7.68

-37.

.30

14)

-7.11

-26.

. 27

15)

-6.62

-19.

.80

16)

-6.19

-15.

.87

17)

-5.82

-13.

.38

18)

-5.49

-11.

,56

19)

-5.19

10)

-10.

.21

20)

-4.92

'-37, 371

The potential will now be set up tor plotting
wave functions; d is automatically started
with vilue of 0 at r-0, as it must be if the
equations are to remain finite with 1/r terms.

Try different energies until you find the lowest
bound-state energy and wave function.

Press RACK when you are done.

\t this point the ^evident is transferred to a part of the lesson that plots nave functions for
various potentials. The potr ial the student just calculated is set up between r = 0 and r *
1«5rmax- Various energies are tried until the wave function shows the proper . asymptotic behavior
at large r. An illustration of this step is shown below in an actual photograph of a student
terminal. The example sho *n does not yet represent a self-consistent wave function.

Step 5:

Here is the you just found, given numerically
at 20 points between r=0 and r=1.5rmax,

<t> is zero at r=0, and is normalized to unity.

r rf(r)

0.15, ...

1.65

0.30,

12)

1.80

0.45,

13)

1.95

0.60,

14)

2.10

0.75,

15)

2.25

0.90,

16)

2.40

1.05,

17)

2.55

1.20,

18)

2.70

1.35,

19)

2.85

10)

1.50,

20)

3.00

The student is given a table of values representing the wave function found in step 4. The
initial and new wave functions are also plotted together for easy comparison. The student hopes
that the two wave functions will be very similar and tries to improve the initial guess until
good agreement is found. Nore steps could be used in the initial guess to make it smoother.

Step 6:

Enter a new guess for ^(r) . I'll give you
the potential to use for finding the new 6.
(Press LAB if you want to change rmax.)

rmax

0 < r

= 2.000

6(z) =

After the student has gone through all of the calculations once, he need not d again unless
he wants to. Only a new guess to the wave function needs to be entered to start the search tor a
new bound state in step 4. The computer calculates the potential. Any of the intermediate
results are available to the student by requesting the appropriate step number on the index
page.

This presents a large portion of the lessons currently being used with physics courses in
quantum mechanics at the University of Illinois. Some lessons attempt to bring to students
knowledge and educational experiences not normally available to them because of complicated
calculations or analysis involved, others provide additional guidance, insight, and exercise in
areas of particular difficulty. All seek to improve the guality of physics education.

37237^

ACKNOWLEDGEMENTS

Appreciation is extended to D. G. Ravenhall for originating the idea for the heli um-a t u .*
lesson, and to B. A. Sherwood for helpful suggestions during the development and testing of tlu:.
and other lessons. Thanks also go to o. K. Campbell, u. E. Kruse, n. B. Salamon, and H.
Stapleton for their interest and cooperation in bringing computer-based education to their
physics classes.

APPENDIX

Below are a few of the homework problems assigned in the junior-senior level quantum
mechanics course. They are to be worked using simulations of wave functions plotted by the
computer.

We 11

Find the energy of the 1 owest-ener gy bound state ("ground state") of a
symmetrical potential well of width 2A and depth -35 electron volts. Sketch the
wave function plotted by the computer.

Find the energy of the first excited state to within ♦ 0.5 eV.

c. Change the depth of the well to -300 eV and confirm that the ground state
energy is near the value expected for an infinitely deep square well.

d. Obtain an estimate for the number of bound state for the -300 eV well. (Hint:
Don^ try to calculate all of them. Use what you know about the number of nodes
in the bound-state wave function of energy En, i.e. the nth bound state of the
system.

Asymmetric Welj

Consider a simple symmetrical square-well potential of width 3A and depth -25 eV with
a small potential "bump11 in the bottom of the well. Two cases are shown, one with the
bump placed at the center of the well, and one in which it is placed at one edge of
the well. ,

a. Find the ground state energy of the symmetrical well without the bum£. Plot the
probability distribution corresponding to this energy.

b. Since the bump is relatively small compared to the well depth, an approximate
value for the ground state energy in :h case shown above could be found from
the sum of the energy in the absence the bump plus the expectation value of
the extra potential energy represent >y the bump. Predict qualitatively, and
justify your prediction in terms of the probability distribution found in (a),
whether the bump in the center has a larger, smaller, or equal effect on the
ground state energy compared to the effect of the bump at the edge.

c. Test your qualitative conclusion in part (b) by finding the actual ground state
energies of the two wells with the bumps shown in the figures above.

Resonance Scattering

Consider ai attractive potential ot depth -20 eV and width 3. 3 % (square well). Study
this potential well for plane waves incident from the left ( with positive energy

373

a. Plot the transmission coefficient calculated by the computer as a function of
energy in the range 5 eV to 15 eV. For what value of B do you find maximum
transmission? What is t*s.e wavelength in the well?

b. Compare your result with the analytic result found in the previous assignment.

Optima* £o&t

In optics it is possible to obtain 100* transmission into a medium of index from a
medium of index n* by applying a very thin coat of another medium of index n2 This
"trick" is used in coated lenses, and

Vfv7

The thickness of ■edius 2 is a, where a = ^2'/4and ^2 is the wavelength of the light
in medium 2. The quantum mechanical analog is shown below.

*■ a +

v=o

Before going to the computer session, try to find a set of values for Va, Vb ,
and E to satisfy the analog of r*2 - v'n i n 3 and also try to estimate the
appropriate thickness, a, for 100* transmission.

With the computer, vary a to obtain optimum transmission, and make a plot of
the wave functions for optimum transmission and of the transmission coefficient
as a function of a around the optimum value.

374

> . i. •

374

INTRODUCTORY QUANTUM MECHANICS AND THE COMPUTER

John R. Merrill
Dartmouth College
Hanover , New Hampshire 0 37 55
Telephone: (603) 646-2977

Int rod uc t ion

Introductory quantum mechanics often is ta irly abstract- The student is immersed in a
melange of new functions and new analytic techniques; he is often not. really at nome with the
mathoma tic:a 1 background assumed by the course. He often feels all at sea- Moreover, the
techniques of teaching guintux mechanics make what seem to the student strange divisions of
material and strange choices ot examples- On the one hand, he is toll how important both the
wave t unct ions and energies for stationary states are, while on the other hand, the emphasis is
on energies alone. The examples ho meets are admitted to be very idealized because they are the
only soluble cases. All-in-all the student gets a peculiar view of quantum mechanics as a highly
abstract, very mu t hemat ica 1 subject dealing with overly idealized physical situations.

When even a small computer is available, there is a wholly different approach to take. We
have been using this approach with sophomores at Dartmouth, and the gain in the intuitive
understanding of quantum mechanics is large- The computer approach uses a simple iterative
technique, is general enough to cover most interesting three dimensional potentials, and easy
enough to understand tor the least sophisticated student- Tne method deals with energies,
wa ve t unct i ons an 1 probability densities simultaneously and on equal footing. It makes the
existence of discrete levels very intuitive- It involves no soph ist ica tod mathematics at all and
yet leaves plenty of places where the analytic approach comes in naturally in a pre-mot l va ted
way.

This paper starts with a short discussion of one dimensional, stationary state, quantum
mechanics at the sophomore level- it then moves on to discuss the three dimensional spherically
symmetric potential- In upper level courses it is natural to follow the material discussed here
with discussions of partial differential equations, and ways to solve the general three
dimensional Schrodinger equation.

The General Method

For stationary state Schrodinger equation problems in one dimensional or spherically
symmetric three dimensional problems, the wave equation can be written (in Hart re e units):

The equation is completely general; any sensible potential can be considered. "

The equation is solved in a simple way very much like an F = ma problem. Fiyure 1 is a block
sketch of the strategy (a simplified flow chart). First, you initialize the wavefunction P and
its first derivative P*, and you choose the energy, E- Then (as the second step) you calculate
the second derivative P" at the point x usiny the Schrodinger equation- You take a small step
ux, and find the new P* and new = ^old + , the new wavefunction P as ^ncw = P + P’Ax f

and the new position as x+Ax « You print out the new position ana wavefunction, an then repeat
tne process (from step. 2) using the new x as the prese : point- Rather than leave the
calcuation as an open loop, you test each new x to see if it is »till inside some preset region.
At the end of the region, you see if the wavefunction is iiverging; if the energy chosen
determines an eigenstate, the wavefunction will not diverge.

As is often the case, convergence is worth worryiny about, especially for potentials which
vary rapidly in x. The simplest method for higher convergence is the initial 1/2 step- This
method is easy to motivate and works for many problems. An even higher convergence method is
sometimes helpful. You can use fourth order Runge-Kutta or predictor-corrector methods.

For the JU problem P(r) = rR(c) (where R(r) is. given in the separation

i|« = R(r)Y™(0,$l) and V(x) = V

effective

375

There is an interesting higher convergence method which is both easy to aotivate and easy
to implement. This "fitting method" uses values of P" at ( n ♦ 1 ) points in the (closed) interval

[x ,x+Ax ]
and P *(

These values are fitted to an nth order polynomial. You then write down the new P,
terms of the integrated polynoaial. If a parabolic fit is used (so that

new

A(H-Al£tA2£2 for 0<£<Ax In [x,Ax]) then
P', . + AO Ax + ^ (Ax) 2 + (Ax)3

old l J

and

P - P . , + P'. . Ax + -^ (Ax)2
new old old 2

+ y (Ax)3 + (Ax)1*

This method is easy to explain to the student and easy to implement (just as the initial halt
step is). The method is also highly convergent: a method with an nth order polynomial fitted to
the second derivative is related to an (n*2)nd order Kunge-Kutta. Finally, the aethod is very

fast on most computers. Simple algebraic expressions are used for a quadratic tit to P"(x),

P"(x+ ■=— ), and PM (x+Ax ) , for example:

Pn(x)

- P"(x+f ) +^f^]/[(Ax)2]
2*[p"(x+ y- ) - AO + ] / ax .

This fitting method has been used successfully with freshmen and sophomores at Dartmouth.

One Dimensional Cases

The strategy of the sophomore course is as follows: We introduce the student to the usual
history of quantum mechanics and to the de Broglie wave picture. We then introduce the one
dimensional Schrodinger equation for stationary states and discuss the infinite square well and
the finite step. These discussions motivate the concepts of discrete state, oscillatory
wavefunction and decaying wavef unction. We sometimes discuss the finite well and oarrier and
state the result for the energies of the harmonic oscillator.

At this point we introduce the numerical procedure. We have the students apply the
procedure to the finite well (whether or not we discussed that problem analytically). The
students then apply the procedure to members of an interesting sequence of potentials V (x) *

| x | m - This sequence has the harmonic oscillator as one member; the harmonic oscillator is used
as a check on the accuracy of the method. The rest of the sequence approximates an infinite
square well with a rounded bottom. The student knows roughly what to expect for energies
and wavef unctions from the simple analytic cases studied. Then the student turns to thr %e
dimensional cases.

All
the fact
parity) .
P'=0 for
out to
wa vef unct
on t.he
wavef unct
number o
found.

these one di
that the wavefu
The students th
even states; P=
large x (well
ion diverges- T
other. The st
ion's tail to e
f 15ops of th

mensional potentials are wri
notions for symmetric cases
en initialize their wavefunc
0, P' = 1 for odd states. The
beyond the classical turn
he wavefunction diverges to
udent brackets eigenvalues
nergy is another indication
e wavefunction inside the we

tten symmetrical
are either even
tionns at the ce
program integrat
ing point) , and
+ » on one side
quite quickly
of the meaning
11 reminds the s

ly in x. We motivate and use
or odd in x (even or odd
nter of the well (x^O) : P= 1 ,
es the Schrodinger

uat

ion

out

the

and

— 0O

ity

the

tes.

The

ate

has

One Jimens iona 1 Examples

Figure 2 shows the ground state wavefunction of a finite well with V0 = ♦100* The
wavefunction is displayed from the center of the well to beyond the edge of the well. The
program can also give P2 directly. The wavefunction is not normalized until the student
calculates I = / P2dx and normalizes the central value for the calculation, P (0) , by 1/ The

energy is 1.07 (from the well bottom) in normalized units; the energy agrees with the analytic

% f

37** 4

solution to better than .1% even for reasonably large step sizes Ax • Changing
♦ 1/2% aak.es the tail of the wavefunction diverge before the edge of the figure.

the energy by

Figure 3 shows the first excited state, which has odd symmetry. Again the edge of the well
is shown- The symmetry is made obvious to the student. The energy again agrees to better than
•1%, and tor a 1/2% change in the energy (E=4.26) the wavefunction diverges before the edge of
the picture.

The hanonic oscillator,
(n+1/2)hw = (n+ 1/2 ) /~2

Figure 4 shows the interesting set of potentials, V (x) = |x|

V (x) = x2 9 is a member of the set, and its energies are known to be E

in these units. As is clear from the drawing, the potentials approximate the infinite square
well out with rounded corners. By observing energies and wavefunction for this set of potentials
as a increases, the student sees progressive effects of the increasingly broadened region where
V (x) 0. The wavefunction can decrease its kinetic energy by spreading out to fill the bottoa

of the well.

Figure 5 shows the grounu states and second excited states (first excited even states) tor
m=2, 10 and 40. The student sees that the qualitative shapes reaain the saae. As ■ increases,
the wavefunction jnust tail off faster in the classically forbidden region. This tends to force
the wavefunction away from the classically forbidden region because the logarithmic derivative
is continuous at the edge.

Figure 6 shows the interesting effect on the energies of the two lowest even states as m
increases. The minimum in Ej near a 5 6 is due to the competition between kinetic and potential
energy terms.

ttany other interesting potentials can be and have been studied, one is the harmonic
oscillator with a Gaussian bump in the center. The states with energies of the order of the bump
size are shifted in energy while higher lying states are left essentially unchanged. This
potential also emphasizes that greater localization leads to higher energy.

A second interesting extension is to the continuum states. Choosing any energy in the
continuum region leads to a wavefunction that does not diverge; the wavef unctions for continuum
states become sinusoidal far from the effects of the potential.

Three Dimensional Cases

r spher

ically symme

trie

three

and

the

d and

£ parts can

be so

lved o

for

e group

of students

. The

most

cau

cast in

to a form exactly

P(r)

rft ( r) w

here R is th

e rad

ia 1 wa

pote

nti

<v<r>

2mr2

The e<

case

scussed

above. The

only

dif fe

case

s (

or f or

non-symaet ri

c one

d imen

its

fir

st aeri

vative at la

rge r

• S i nc i

asy m

pto

tic sol

utions (when

|v|<

<|E| > 1

The

udent

initializes

the

funct

int e

gr a

te back

toward r -

0 ste

p- b y-s

i>0

the wa

vefunction

P mu

st go i

fin i

at r =

dimensional potentials, the Schrodinger equation separates,
nee and for all - numerically or analytically as seems best
important part is the radial equation. This radial equation
that of a one-dimensional potential by the substitutions:
vefunction. The potential is replaced by the effective

guation is solved in a way analogous to the one dimensional
rence lies in the initialization. For three dimensional
sional cases) , the student initializes the wavefunction and
e, for all interesting cases, |V(r)|+ 0 as r^° tne

P “ e'/2lEl r and P’ « - /2|e| e~'^^T
ion at large r, chooses the energy and has the program

tep.

The student checks the wavefunction near r = 0.

For

to zero at r = 0. For

£-0

both P and R = P/r must remain

Three Dimensional Examples

The strategy is completely general. The student can, if he wishes, use the numerical method
on the hydrogen atom. The energies agree to better than .1%, and the radial wavef unc t ions , R,
are indistinguishable from those of the analytic solution. Other interesting examples include
the screened Coulomb potential and the 6-12 potential-

Figure

7 is

a plot of the 6-1

2 potential

V (r)

= 400 (p*2- 7T )

and

the energies of

the

lowest three

i =

0 ( s) states.

r i

Figures 8, 9

and

10 shovf the vavefu

act ions

= rs

for these states.

energies

are -6b

.2,

-22. 9, and -4

. 1.

The hori z onta 1

scales

t he

figures are all

the

same so

that

the

wave funct ions and the potential can be directly compared.

-r/10

A second example is the screened Coulomb potential V (r) = - - —

• Figure 11 shows

ERIC

377

SC HR OD I NGER_ECI
SET I N I T I A 1 P,P'

SET ENERGY

CALC. P'(X) (SCHR.)
CALC. NCW P'=P'+P'AX

FIGURE I, Block diagram of an iterative solution
to Schrodinger 1 s equation.

FIGURE 2. The ground state of the finite well.
Only half the wavefunction is sh^ m, namely that
for x>0.

FIGURE 3. First excited state of the finite well.

FIGURE 4. Members of the series of potentials
V (x)«xm for m*2, 6, 10, 40 and infinity.

4) *

fS-3

• C

o <u

r-l U
O

(4 a
os

-a

(S.2

g a

^ a

a r-<

380

FIGURE 11. The radial vavefunction, R, (and x=rR) FIGURE 12. The first 1=0 excited state of the

of the ground state of the screened Coulomb poten screened Coulomb potential,

tial V(r>* - exp(-r/10)/r.

FIGURL 13. The lowest 1=1 state of the screened
Coulomb potential.

FIGURE 14. The lowest 1=1 state of tne (more
tightly) screened Coulomb potential 1 (r)»

- exp(-r/5)/r.

381

R and P = rR tor the lowest energy s state (£■()> • This ground state has an energy of E s -*40d
(as con pared to an unscreened Coulomb ground state of -.5 in these units). The wave f unc t ions,
particularly for higher lying levels, are noiice*bly push'd towards r = 0 coipared to unscreened
wavef unctions. Figure 12 shows R and P = rF for the first excited t-0 state; the energy is E =
-.OSd compared to an urscreened energy of E - -.125. Pol the unscreened Couloib case, this state
is degenerate with the lowest lying f-1 (p) state. Figure 13 snows R and P for this lowest p
state. Th<> energy for the screened case is E = -.047, so the state is not only shifted but th r
degeneracy ls broken, too. This is one of the striking effects of breaking the strict 1/l
dependence, A second striking effect is shown in Figure 14. This shows the lowest energy p state
for V(r) = e~r/ (tighter screening).

state is just barely caught with an energy of E = -.0043. It is the only p state caught by
the potential.

Conclusion

In upper level courses you can go fro» these examples to discuss partial differential
equations and the solutions to the full Schrodinger eguation. This is appropriate for a junior
or senior level course. The di^ussion above has proved very effective at the sophomore level -
the first introduction to quantum mechanics and the Schrodinger equation.

We have used this approach both in regular lecture courses anl in self-paced (Keller Plan)
courses. The system works well in both situations. The students gain considerable intuition ir
quantum mechanics. They can routinely sketch wave f unc t ions and guess approximate energies for
states even in complicated potentials. This is a very useful application of computers to
educa t ion.

* .

382

INTERACTIVE CtASSBOOfl GRAPHICS*

Tia G. Kelley
Southern Oregon College
Ashland, Oregon 9752^

Telephone: (503) 482-64* °

Dafid Grillot, Jeffrey D. Ballance, and tarry R. Hubble
Oregon state University
Corvallis, Oregon 97331
Telephone: (503) 754-1631 and 249':

15 1 CQ Auction

In previous papers (1,2) a pilot project was described which wjuld allow an instructor to
present coiputer-generated graphic intonation interactively in t!ie classrooa. In (1) the
software requirement for such a systea were discussed and in (2) the use of the systea for
production of visual aids (35 aa slides) was described. The software systea, which has been
naaed GROPE (Graphic Representation of Paraieter i2ed Expressions), as run on-line using the
tiae-shared Oregon State University CDC-3300 co-puter. The systea has as its underlying
instructional philosophy the enhanceaent of the students* appreciation of various paraaeters
which enter into a problea*s foraulation. Thu<; GROPE has been structured to develop and display
paraaeter ized faailies of curves. There are various aethods available for defining these curves.

In the vast aajority of cases, GROPE can be utilized effectively by a prospective teacher-user
who has no previous coaputer experience or knowledge. While in the classrooa the instructor
issues siaple aneaonic coaaands via a keyboard and the resulting graphic inforaation is
displayed on T. V. aonitors or on an ordinary projection screen, since an unliaited nuaber of
coaaands caa be issued, displays nay be continually developed, augaented and aodifiod.
Purtheraore, since the coaputer noraally responds to these coaaands in seconds, the tiaing and
sequential structure of : he displays aay be controlled. A systea which has these features
provides a viable tool to suppleaent classrooa lectures

It is the purpose of this paper to describe: (1) the hardware configuration necessary for high
quality classrooa display, (2) the classrooa use of GROPE in the Oregon State University Physics
Departaent, (3) soae ex; wples of its capabilities.

Hardware

A hardware configuration has been achieved which allows GROPE to be used interactively in
any si2e classrooa. In addition to the tiae-shared coaputer, the hardware consists of the
following equipment:

1. 4002A Tektronix Coaputer Graphics
Display Terainal (Tekter ainal)

2. 4501 Tektronix Scan Converter

3. A-912 ACP Kalart Tele-Beaa or T.V. Monitors

4. Graphic Input Device (Joystick) *

The total cost ot these iteas is roughly $15,000 excluding coaaunicat ion costs. (With the advent,
of less expensive terainals this cost is reduced to roughly $10,000.)

The Tekterainal, which provides the weans o
which converts digital inforaation to analog output,
froa one classrooa to another. The Tele-Beaa,
inforaation onto a projection screen so that graphic
lecture rooas. In saaller classes (less than 15
Monitor. Since the equipaent is easily aoveable, the
before a lecture is less than 5 ainutes.

£ input and output, and the s;an converter,
both reside on a cart which can be aoved
which is also aobile, projects the analog
displays are easily viewable in large
students) the Tele-Beaa is replaced by a TV
tiae required to set up the apparatus

This project was supported in part by NSF Grant GJ28453.

383

Figure X shows the arrangements of the equipment in an actual classroom use*

classroom Use of Grope

Host of the faculty members who are using GROPE have had little or no experience with
programming languages and computers. One of the primary considerations in designing the software
was that such an uninitiated group be able to both learn and use the system in a minimal amount
of time. The typical instructor spends less than one hour reading a manual and after two hours
of assisted practice he is able to employ GROPE in his lectures even though he has acquired only
a rudimentary knowledge of the capabilities of the system. More sophisticated use of the system
develops rapidly as the instructors need arises.

The response of faculty members using GBOPE in courses at all levels has beeu enthusiastic.
Large numbers of physically interesting problems which would be either impossible or difficult
to analyze without the use of a computer are now routinely being exanined in detail in various
courses. The instructors find that not only do their students learn, but surprisingly they
themselves gain new insights into the subject matter as they prepare their graphic
presentations.

GBOPE became classroon operational the last half of Fall quarter 1971. Since that time it
has been effectively used in the following courses at Oregon State University:

•' i.

38'S8"

£ aiuaa JLfii

Abridged Gt&tctl Phyaica

Description

General Survey courae for atudents with little
aatheaatical background

General Phyaics

General Survey cobra* foe students having had collage
algebra and trigonoaetry

General Physica
Physics 1

General Survey course for freshaan engineers

Introductory physics for freshaaa phyaica atudents

Mechanics

Undergraduate aechanics course for junior aad senior
physics students

floderu Physics

Selected topics in aodern physica for senior physics,
engineering, and cheaiatry atudents

Oynaaics

First year aechanics course for physics graduate
and advanced undergraduate students

These courses were selected to initially test the feasibility of GBOPE for classrooa use, and
efforts are now being directed toward expanding its use into other disciplines*

gftMfehJLitjga fiaiplfi

In order to create on-line classrooa displays using GBOPE, it is first necessary to define
functions aad then to specify the types of plots to be generated*

Functions nay be defined in any of the following ways:

It is also possible to define completely new functions in terns of one or sore previously
defined functions*

After the functions have been defined, they aay be displayed in various ways* The following
list exhibits soae of the possibilities:

The reaainder of this section consists of exaaples which are intended to illustrate the
instructional value of a systea with these capabilities*

SxaiPl* 1: Us Bgttflalltf

The over-siaplif ication required to achieve analytic solutions seriously handicaps the
teaching of aatheaatical aodelling for realistic systeas* \'he reaulting disagreeaent between
aodel predictions and experiaental reality is disconcerting to beginning students. Often they
feel a disenchantaent with aatheaatical analysis, since it seeas incapable of dealing with "real
life" probleas* This is particularly true whenever the aodelling is done through differential

1* Typing analytic functional foras*
(These aay have different foras in
different doaains.)

2m Typing coupled differential equation sets.
(See Appendix for the nuaerical aethod.)

3. Interfacing subroutines to GBOPE*

1. Cartesian or polar coordinates

2. Paraaetric or non-paraaetric plots
3* Multiple curves on the saae axis

4. Two sets of axes on the saae display

5. Powder plots of one or two diaensional

distribution functions

equations. A lore serious consequence is that students do not begin to learn the process of
successive model refinement until late in their training.

As a simple example of how interactive graphics can help to alleviate these shortcomings,
consider the one-dimensional pendulum problem. One begins by neglecting friction in the
mounting, finite size of -he pendulum bob, mass of the rod, rotation of the earth, etc.; in
short, everything except the downward force of gravity. This is as it should be; the initial
model should be kept as simple as possible. Even so, the resulting form of the equation of
motion for the angular position of the bob,

x" ♦ sin x = 0,

has no known analytic solutions.

Practicality often forces a serious pedagogical error at this point. Tor small angles, the
repiacenent of sin x by x allows a solution to be obtained, but the validity of the
approximation is far too difficult to evaluate at introductory levels. This is an unfortunate
precedent to set, especially as it may be a students first encounter with making

approximations. A graphic presentation provides an excellent evaluation of the approximation.

and can be understood

and appreciated

by students at

all levels.

Additionally, an

in ter active

approach allows

participation .

t he

analysis

take on the

f la vor

in v est iga t ion.

with class

The problem

initiated

typing the sequence

(Input

typed by the

instructor is

under 1 ined. )

YjT) = A*C0S ( T)

A = .2 BY .2

(Carriage Return)
X = -_2_0Y_. 2

X* = 0

hich defines the harmonic solution Y (T) , and defines X (T) through its differential equation and
initial conditions. The va'ue of Parameter (A) and initial conditions U and X1} are requested
by the computer. Since we already know that the validity of the approximation depends upon
smallness of angle, it would be mos* useful to generate a family of plots, parameterized by the
amplitude of oscillation. Hence, A and X are established as automatically varying parameters by
the above sequence. Following these definitions a series of commands must be entered to specify
the functions to be plotted;

PLOT. Y

SPLIT. HOBIZOHTAL
PL0Tt X .

After providing information requested by the computer concerning the ploting ranges. Figure 2 is
obt ained.

FIGURE 2

FIGURE 3

386

It should be emphasized that these input sequences are entered on-line and would completely
define the problem to the computer. Jig py^or preparation necessary. In fact, it can all be
done right in the classroom because it would take no longer than 30 seconds to enter dll the
necessary information and to get the first graph.

Eac^ successive curve in the families is generated by depressing the carriage return key.
Figure 3 night eventually be obtained, which shows very clearly the qualitative difference
between X and I: The period of the harmonic Y is independent of the amplitude, whereas the
period of the solution X for the real pendulum increases with amplitude.

To obtain a more quantitative comparison both X and T could be displayed on the sane graph.
The graph format can be respecified by a PLOT command without redefining the function, so Figure
4 can be produced in a natter of just a few seconds. A provision also exists for skipping over
the range if the previous ranges an still satisfactory. For classroom use all shortcuts becone
important to minimize delays in the presentation. For this reason all command words (like PLOT,
SPLIT, and HORIZONTAL) can be abbreviated by their first letter.

At this point the goal of obtaining a visual evaluation of the approximation has been
accomplished. A good idea of the angular range of validity can be obtained, depending upon the
accuracy required. It would be difficult not to notice, however, the striking resemblance of the
real solution X to another cosine cur- e which is just frequency- shifted. This is an unexpected
result that a cuLious student should want to investigate further. Why not "measure" the shifted
frequency and compare X with a cosine curve of that frequency, as a further check? The
coordinates of the appropriate points are requested by means of the "Del" command which employs
the graphic input feature (see ref. 2), and within seconds the period of X is established to be
6.72 for the A= 1 curve. Typing

then adds this curv? to the disolay, producing Figure 5. The f requency-shif ted -osine is truly a
remarkable approximation to the real solution X.

Computer graphics has thus guided us (the class) naturally to an important conclusion which
could not otherwise be reached except through a tedious laboratory exercise. Furthermore, the
appropriate language for concisely formulating the evaluation criteria is now clear. A table, or
perhaps a graph (♦), of the frequency shift versus amplitude would provide a quantitative measure
of validity. Figure 6 shows that this approach would be adequate up to an amplitude of about 2
radia ns.

FIGURE 4

FIGURE 5

PLOT , A»COS (2+PI+T/6 ,72)

This particular graph cannot be generated
on-line without prior preparation. A subroutine
would have to be written and interfaced
co GROPE, which would allow it to be
referenced in GROPE through the XTERNAL
command. The interfacing amounts to
placing the object deck of a function
subroutine on magnetic disk file.

387

A slightly aore ldvanced student Bight well be motivated to ask whether a correction so

bit of insight is needed to get started. The first step is obvious, namely, use a better
approximation for sin x. To bolster confidence in the usefulness and validity of such a step,
one might define X A (T ) ( "X- Appr oxima te") through the differential equation

and compare X A ( T) with X (T) for a large amplitude, as in Figure 7. The difficulty now is 1ft
treating this equation, which also has no known analytic solutions. Here is where an interactive
graphics system can be used advantageously to assist and guide in sharpening analysis. The work
thus far has suggested that XA is well approximated by the fori cos(wt) , where w is a shifted
angular frequeuc . To establish this requires that the difference between XA and cosfwt) be
shown to be "saaliM in comparison to cos (wt) . The standard aethod is to "guess" (by trial and
error) an approximate form for the difference and then determine relative amplitudes by
suostitution into the differential equation for XA. Since the trial and error process would
require an hour or two for even good students, the guessed fora see as to a class to be "pulled
out of the air." But GROPE can readily generate XA(T) and plot it, so a natural attack is to
plot the difference of XA (T) and A*COS(W*T) , in the hope that it will have a simple enough form
to recognize. (At this point the class or even the instructor may have no idea as to the size of
this difference except that it is small. An automata scaling feature wherein GROPE scans the
data to determine appropriate axis limits for dependent variables is very helpful in such
cases. )

The plot of the difference function shewn in Figure 8 actually contains the needed
information, but inf ort una tely it is not as recognizable as it might be. Because A and 1(0) have
been chosen to be equal, the difference function as defined necessarily vanishes at T=0. This is
arbitrary, and it is not unreasonable to hope that relaxing this restriction might yield a more
recognizable fora. Accordingly the function

plotted, with B varying. The scale of the variation in the cosine amplitude was suggested by the
"size" of the function plotted in Figure 8, Figures 09 and 10 reveal the answer. At B=6 the
difference function is very recognizable as cos(3wt), suggesting that

be substituted, with a, b, and w to be determined. HUon the analysis is completed (3) the

be very snail in comparison with a. The result for w is al:»o in quantitative agreement with that
obtained graphically.

simple in nature cannot be deduced directly fron the aathematics. Indeed there is a way, but a

XA" (T) * -XA + XA^ 3/6

Y (T) = ( A ♦ .00 1 *B) ♦COS (2»PI*T/T0)

was defined, and

D(T) = XA - Y

XA = a cos(wt) ♦ b cos ( 3 w t )

mathematical support for the conclusion that X = a cos (wt) is indeed found, since b turns out to

FIGURE 6

FIGURE 7

388

FIGURE 8

FIGURE 9

FIGURE 10

) # *
* J ?

389

369

There are obviously a large variety of comparison curves which a student sight now be inspired
to reguest of the instructor* A real advantage of an interactive graphics system is the
encouragement of curiosity* For example, we are now ready to successively refiQe our model by
incorporating the frictional terms, etc*, that were neglected earlier. Once a refinement' is
decided upon, the effect it has on the solution can be seen immediately.

Example The Spherical gendujgf *

One of the more pleasant surprises has been that instructors and students alike gain deeper
insights into their subject material by the use of graphics. By being able to view "exact"
solutions to problems under conditions where usual approximations fail, a new perspective is
often acquired which leads to a more refined mathematical analysis.

A good example of this is the ideal spherical pendulum. It is just like the simple pendulum
of the previous example, except that the bob is free to move anywhere on the surface of a
sphere. Although solutions for special cases can be exhibited, the differential equations have
in general oo known analytic solutions.

The usual analysis (4) assumes the notion to be nearly circular, and yields a notion whose
projection onto the horizontal plane is approximately that of a processing ellipse as in Figures
11 and 12. The development of an expression for the precession rate is long and difficult for a
student to follow, often because it is not clear where the analysis is leading. If a few
accurate examples like Figure 12 for different rates of precession are shown to him, then he can
see from the start that i*he salient features of this systematic motion ought to be extractable
from the mathematics. Then when the approximate precession rate is obtained, it (1) is clear
what it means, and (2) can be compared with that shown graphically.

FIGURE 11

FIGURE 12

The differential equation set could be specified to GBOPE in whatever coordinates are
convenient, but they are simplest in cartesian coordinates. The sequence.

x* cr\ z z£tF

YM(T) - -T»P
£”1t) - -Z»F - G

F(T) == [X*~2 4- Y'~2 + Z'"2 - Z*Gl / L 2

which would be followed by reguests for the initial conditions and the parameter values for G
a^d L would completely define the problem. Then the command

Ek21±UlL

produces the parametric plot of the motion projected onto the I-T plane. Bealism might be added
by including frictional terms, -B*X«, -B*Y f , and -B*Z#, in the first three of the equations,
yielding a result typified by Figure 13. Simple commands exist for printing function definitions
and parameter values so the student n«ed never wonder what functions are being displayed.

3S0

FIGURE 13

FIGURE 16

FIGURE 15

FIGURE 18

391

* t i

'• ■ * .«

391

Returning to the friction loss case, incrossing the energy (by iscrosoing incrosoos
the site of the orbit until it is no longer 19 nearly circular,11 and the 1-: projection of it is
no longer siaple. one of the nore powerful features of interactive graphics is the ease with
which one can eianine different aspects of a problen in search of a better perspective* Th^re
are a great nany possibilities, of course, but it turns out that the nost obrioss ones lc;d.to
success* In particular, even though the X (T) and t (f) notions are sonewhat con plica ted, as shiwn
in Pigure 14, the Z (T) notion is anazingly harnonic at all energies. This is illustrated jin
figure 15 which has graphs of Z (T) at three energies: a low energy, corresponding to the
processing ellipse; a high energy where the kinetic energy greatly exceeds the potential energy;
and one in between. All appear very harnonic, although the internediate energy curve contains
considerable second harnonic conponent.

one of the pedagogical values of the spherical pendulun problen is the opportunity it
provides to illustrate the use of conservation principles to extract pertinent features of the
notion. Having thus been led to a view of the notion that is sinple, these principles can now be
used to understand why. If V2 * X**2 + Y'* 2 + Z'*2 J^a eliminated from the equations of motion by
conservation of energy, the Z" equation provides a full explanation of the harnonic nature of Z.
Even though X« and Y” are not sinple despite replacing Z by a harnonic forn, the constraint
equation yields a sinple forn for p2 * X*2 + Y*2 • For large Z-osci Hat ions the axinuthal notion
can then be obtained by using conservation of angular nonentun. The result of the analysis shows
that the I- Y notion again approaches that of a processing ellipt>e at high energies, but the
piecession is in a direction opposite to that at low energies. The exact solutions displayed
graphically can then be used to verify these conclusions.

There are at the sane tine violent oscillations of the 2-coordinate. To help visualize the
full notion, the projections in two perpendicular vortical planes can be displayed, as in
Figures 16 through 18. Perhaps a better view of the notion is attained by typing in a few nore
equations to generate a 3-diaensional isonetric representation of the notion, as in Figures 19
and 20. In all these cases the classroon presentation is far clearer than the pictures inply,
because the dynanics of developnent are not lost. For exaaple, the two curves of each of the
split- plots of Figure 16 through 18 develop alnost at the sane tine, so that the correlation
between the l wo is clear.

All the curves shown were generated fron functions defined on-line, including the isonetric
circles portraying the sphere. A total of 14 different functions had to be defined, and it is
not practical to try to type that nany equations in a classroon situation no natter how well-
rehearsed the instructor is. To avoid undue delay when atteapting conplicated problens like this
a FILE coasand is included for saving the definitions on d. sk file* The FILE connand can be
qiven at any tine and will save sufficient infornation to later restore the systen to its
present status. The GET connand nay be used later in class to retrieve this infornation. After
the GET connand is issued there are no restrictions in the use of GROPE and the instructor is
free to utilize its full interactive capability.

5i§§r1§ ll Schroedinqer Equation- Powder Plots

Another area for potential use of conputer graphics is in clarifying the neaning of
functions of nore than one variable. The present exaaple is concerned with pictorially
representing wavef unctions of the 3-diaensional Schroediager eguation. For a broad class of
potentials (5) , the wavef unction can be written as

where the angular functions, p£m(0)' , are the associated Legendre polyaonials, and

Un| (r) * rRnt(r) satisfies the second order differential eguation.

for the radial eigenfunctions.

The technique and instructional value of searching for the eigenvalue and eigenfunction
which satisfy the radial equation and the appropriate boundary conditions have been discussed
elsewhere (6,7) • Figure 21 shows the final result of ^uch an interactive trial and error search
for the correct eigenvalue, E, and oigenf unction U-j 3 . After U^(r) is deternined, the
instructor can easily display both the radial density 2 and the angular density on the
sane screen as shown in F*~nres 22 and 24* As . n Exaaple 2, the connection of these 1-
diaensional representations and a neaningful 3 tiinensional picture of the physical reality is
difficult to nake without the aid of graphics. This connection can be aade pictorially by
generating a 2-diaensional powder plot representation (7) of the distribution functions,
!R13* 2 p30 2 & IR13| 2 lp33l 2 45 shown in Figures 23 and 25. These figures illustrate the

■ *nl<r> p£s,(9)eim^

392 392

FIGURE 22

FIGURE 20

FIGURE 23

FIGURE 21

ERLC

393

Uv. U

FIGURE 24

FIGURE 25

d is tr ibu t ion
polar-ax is.

function as a thin cross-sectional slab of uniform thickness which contains the

By using these figures and standard classical arguments the qualitative relationship
between particle distribution and the projection of angular loientui can be clearly illustrated.
For lower level non- technica 1 students the powder plot provides a vivid method of introducing
difficult elementary quantum mechanical concepts such as probability density.

The advantage of interactive graphics at this point is, as mentioned earlier, the
flexibility and ease with which the instructor may pursue variations in this problem. He nay
c'aoose to examine the effects of changing the strength or range of the potential on the particle
distribution for the previous eigen states, or alternatively, he could choose to examine a
completely different radial eigen state. These choices may very well be initiated in response to
student questions. Figures 26 and 27, which represent the distribution function for an N-0, L=3,
n=0 state, might be the result of such au extemporaneous classroom discussion.

FIGURE 26

FIGURE 27

394

4i *£12 liSlSL 1 Ssssuasiioi!

The properties and behavior of localized wave packets are obscured by mathematical
complexity. A graphic representation of the mathematics is very appropriate here, and the
complexity makes computer generation the most practical, if not the only, way to achieve
clarity.

Formally, a wave packet can conveniently be expressed as an integral

yk (x,t) = / A (k - kQ) cos(kx - wt) dk

o *

-o o

where A must be a square integrable function. A (k) is peaked at k=0 and is usually characterized
by oone measure of its width. The frequency w is in general dependent upon k, and it is
generally instructive to express w as a power series in (k -kQ)‘ . To acquire a full

understanding of the packet construction and its tine development, a student needs to appreciate
how y^ depends upon the coefficients in this series, the width and shape of A, and the
central component kQ . The analysis of these characteristics could be achieved in the standard
way using features of GBOPE which have been discussed earlier. Consequently, we will not delve
into these details here. Instead we wish to concentrate on the difficult and important concepts
of phase and group velocity which often remain hazy for many students.

FIGURE 28

FIGURE 29

After A (K) and 0(K) are defined, Y ( X) could be defined in two more steps,

F ( K, X) = A (K - K0)*C0S(K*X - 0(K)*T)

Y (X) = I NT (F, L, U , H)

where INT is an internally defined function which numerically approximates ) F(K,X)dK
using N integration intervals. L

Figures 28 and 29 show the propagation of a packet from T=0 (dashed curve) tr T=5 (solid
curve), and compares it with the propagation of the central couponent. To make the distance
travelled apparent, the latter wave train was truncated outside a small region, as follows:

Z(X) = C0S[K0»X ~ W(K0)»T] IF -5*PI/2<KO»X - W(K0)»T <5»PI/2 ; 0

Z then has the cosine form only if the argument of the cosine lies between -5n/2 and 5n/2 ;

otherwise it is zero.

These Figures show clearly
velocity, the latter being equal to
The "spreading*1 of the packet,
apparent •

the distinction between the phase
the coefficient of the linear term in
caused by the higher order terms in

velocity and the group
the expansion for 0.
the expansion, is also

395

3*5

lhere are a number of
introducing different foras for

physically
W (K) .

interesting cases

which could then be examined by

ACKNOWLEDGMENTS

Tae authors wi5h to than!; the staff of the OSU Computer Center. We are particularly
indebted to Dr. L. c. Hunter* Mrs. J. Baughman, and L. Ochs for their assistance, cooperation,
and suggestions. Nuaerous members of the OSU Physics Department have aade valuable suggestions
in desiguing the systea. Dr. P. Ft. Fontana and B. Srivastava have been particularly helpful and
exceptionally patient in suffering through nuaerous revisions of the system. We also gratefully
acknowledge an educational grant froa Tektronix, Inc.

REFERENCES

1. Kelley, T. G. , "On-Line Classroom Graphic Displays," in Proceedings of the

Conference on Coaputers in Undergraduate Science Education, ft. Blum, Editor,
Coaaission on College Physics, 1971.

2. Kelley, T- G. , "A General Graphics System for Computer Generation of Visual
Aids,1* in Proceedings of the Second Annual Conference on Computers in the
Undergraduate Curricula, A. Luehrmann, Editor, Dartmouth College, 1971.

3. Kittel, Charles, W. D. Knight and M. A. Budernan, Mechanics Berkeley Physics
Course 2 Volume J., McGraw-Hill, New York, 1965.

4. Fowles, Grant B., Analytical Methods, Holt, Rinehart, and Winston, Inc., New
York, 1962.

5. Leighton, Robert B. , Principles o£ Modern Physics. McGraw-Hill, New York, 1959.

6. Luehrmann, A., "Instruction Uses of the Compater," American journal of Physics.
March, 1967.

7. Ehrlich, H. , "Physical Simulations for an On-Line Computer-Controlled
Oscilloscope," in Proceedings of the Conference on Computers in Undergraduate
Science Education, R. Blun, Editor, Commission on College Physics, 1971.

Q. Hamming, R. W. , Numerical Methods fpr Scientists and Engineers. AcGraw-Hill,
New York, 1966.

9, Ralston, A- and Wilf, H. S.# Mathematical Methods fo£ Digital Computers. Wiley
& Sons, New York, 1960.

APPENDIX

Solutions to the differential eguations are computed using Ada ms-Bashf or th-Moulton
predictor-corrector formulas. The formulas ha^e error terms o(h~’) which are reduced to
0(h6) by using the difference between the predicted and corrected values as a correction on
each’ step. The difference between the predicted and corrected values is also used to control the
local error. If this difference becoaes too large the step width is halved and the calculations
repeated using the new step size; if the difference is too small the s tip width is doubled and
the calculations continued. Since the step width is allowed to change as needed and plotting and
oth*ir calculations are done with a fixed increment, the solutions at the reguested points are
not always available. when this condition occurs the reguested values are calculated using
available values and an interpolation formula with error U -m 0(h6) . The starting values for
the predictor-corrector method are computed using Bunge-Ku ca-Giil formulas. The first value is
calculated using a stepwidth which is halved until the difference between the values computed
using a given stepwidth and those computed using half that stepwidth is very small. A discussion
of the aethods used is given by Hamming (1) and by Ralston and Wilf (2).

316

396

CODPUTER GRAPHICS IN PHYSICS

Herbert leckhan
Garilan College
Gilroy* California 95020
Telephone: (408) 842-8221

It is very useful to construct a picture of a phenomena* nathenatical relationship* or
process. The problen occurs when one attempts to do this. The diagrams drawn on a plane (a
blackboard or sheet of paper) rarely look like the real thing. Therefore* it would be highly
desirable to find a Method to generate such pictures which would appear exactly as if a real
physical representation were viewed with the eye. T» e digital computer furnishes such a
capability when progressed to carry out a projective transf orsation. This paper will develop an
approach to projective transf or sat ions and will exasine several applications in physics. A BASIC
progras is git n to carry out the projection.

The idea 0£ A Projective Transiorsation

A nu.iber of ways exist by which an object in three spa i can be developed or projected upon
a olane. The casera is probably the sost common. Says of * ight cosing fros the object are
projected by the lens upon the projection plane which in this instance is the fils.

The strategy which will be developed in this paper is guite different. The concept is
portrayed in Figure 1. The process is described with respect to a cartesian coordinate systes.
The observation point is located sosewhere in space with a line of sight directed towards the
origin. Isagine that the object to be projected is described by a large nusber of points (x, y,
z) one of which is shown in the diagras. if a ray is constructed which passes through the
observation point and the point to be projected* the point of intersection with the projection
plane can be found. If such a ray and corresponding intersection is constructed for each of the
points on the object* the object itself caa be developed on the projection plane.

Projection Plane

Figure 1

3S7

Hatfre yatxcal peveloppept of Intercept Point

Proa the aatheaatical point of flew, when an observation point (x0,yo,z0) and a
projection point (x,y,z) are fixed, the intercept point (x^,yi,zi) on the projection plane
is uniquely defined. The problea is to locate the intercept point in teras of the coordinates of
the observation and projection points.

The direction nuabers of the line of sight joining the origin and the observation point are
the coordinates of the observation point itself. Knowing these direction nunbers, the equation
of the projection plane (the plane passing through the origin aid perpendicular to the line of
sight) can be written. If this equation is written in terns of the variables (xifYirzi) the
result is

x . x
1 o

+ *1*0

The direction nuabers of the projection ray passing through (x0,y0rZ0) and Lx, y,z)
are: (x-xQ) « (Y**Yo) * and (z-z0) • Note that for the purposes of each projection,

the coordinates (x, y, z) are assuaed to be constant. The equation of the projection ray which
has the direction nuabers above, and which passes through the point (Xo,yofZo)

If (1) is solved for the result is

But from (2), y ^ and Z£ can be written in terms of If these substitutions are aade in
(3) , the resultant equation can be soLved for xi • Since there is nothing unique about the z.
coordinate of the intercept point, the other values and z* can be written from symmetry.

-(yp + zo)x + (y0)y + (xozo)z ■

X1 = x0(x - x0) + yo(y - yo) + Zq(Z - zq) ’

m (xoy0)x ~ (xo + zo>y + (y0zo)z
Xl “ xo(x - *0> + y0(y - y0> + z0(z - zQ> ’

_ (xqzq)x + (y0z0)y - (X* + y\)z

Zj- = x0(x - xo} + y0(y - y0> + z0<z - z0> ’

Equations (4), (5), and (6) describe the intercept point. However, since the objective is to

develop the point on a plane, a transformation oust be written to transfora the point in three
space to a point in two space (the projection plane) where the point can be located by two
coordinates.

Transformation of Intercept Point Froa e3 to £2

One way to carry out the desired transf oraation is to locate a pair of orthonoraal basis
vectors in the projection plane but which are still described in . If a vector is constructed

398

fro* the origin to the intercept point (also described in ) then the inner product of this
vector with each of the basis vectors gives the coordinates of the intercept point in which
can then be plotted.

An infinite nunber of sets of basis vectors for the projection plane can be found. The
desired set is that one which does not result in a rotation of the object. One way to locate
this particular basis set is to project the unit vector in the z direction (0, 0, 1) onto the
projection plane. Since (0,0,1) corresponds to "up" with respect to the object, the projection
of this point onto the projection plane will locate the proper "up" direction in tue development
of the object. Let the projection of (0, 0, 1) onto the projection plane have coordinates
( x ' ,y ' , z * ) . The (4), (5). and (6) yield

or, if

the n

Thus, if

then a unit vector in the "up" direction in the projection plans is

ERIC

399

The unit vector fron the origin towards the observation point is

where Rj is defined by (7). U2 is one of the required set of basis vectors. If is the

other, it is defined by u| = U3 x ^ » or

2 v_ -
o 2

R1R2

yoV3 ‘ , xoV3 ’
x +

2 V1
o 1

yoVl -

x V,
o 2

R1R2

Let

►

}

and

projected plotting coordinatesj

X ■ x^x + y^y + 2^2 a intercept point.

Then

and P„

In natrix notation

P = TX

where

2 V. -
o 2

yoV3

x V„
o 3

2 vi

o 1

y0Vl '

XoV2

R1R2

400

Ifci £fit£jils£ ftaatai

Mots that the projection divides readily into two sections, (first, specification of

(Xo,yo»*o> defines the transf or sat ion natrix T. This reaaias constant for a 9ivea prohlea. The
second part of the projection involves conputation of the intercept point. Since this depends
upon the projected point (x, y, z) it nust he done for every point to be projected.
Consequently, this should be bandied an a subroutine. The BASIC language progran to carry out
the projection is sboun in Figure 2.

LIST

11 REN SET V OBSERVATION ROUT

IE RRUT "IRRUT OBSERVATION ROIMTt

14 URUT Xf.YG.ZG

1C REN OONRUTE TRANSR0RNAT10N NATRIX T.

15 DU T(2»3)»R(2 ),I(3 ;

20 LET Rl xSORfXf T2+Y* tt-f ZR t2 )

22 LET VI t-XN*ZN/(RI t2-ZG >

24 LET «s-YN*ZN/<Rl f2-ZN>

2C LET V3t<XNf2+YNf2>/<RI f2-ZN>

28 LET R2sSGR(V|f2+V2f2+V312>

SO let TU,l)«ZO*W-YO*V3>/<R!*R2>

32 LET T(l,2)*<XG*V3-Zf*Vt>/<RI»R2>

34 LET T(l,3)«YB*Vl-XS*Ue>/<RI*R2>

34 LET T(2»llsV|/R2
38 LET T(2,2)sV2/R2
40 LET TI2,3)=V3/R2
42 REN END OR CONRUTATION OP T.

44 00T0 US

M REN SUBROUTINE TO CONPUTE INTERCEPT
92 REN AND PROJECTED PLOTTINO POUTS.

94 REN POUTS TO BE PROJECTED NUST
94 REN BE DESCRIBED BY <X,Y,Z>.

98 LET R3:XN*<X-X0>+Y0*<Y-YN»Z0*fZ*ZS>

40 LET HI )s(*(YB«2+Zif2)*X+XS*YB*Y+XNsZS*Z)/R3
42 LET I(2):<XG*Y0*X-<XN«24>ZG«?>*Y+YB*ZN*Z>/R3
44 LET l(3)s<XN*ZN*X4>Y0*Zf>*Y-(XBt2*YBt2>*Z>/R3
44 HAT P-Ttl

48 REN END PROJECTION SUBROUTINE. PROJECTED POINT
TO REN CORRESPONDING TO CONPUTED POINT(X»Y,Z> HAS PLOTTING

12 REN COORDINATES (P1,P2>. IN CALLUO PROGRAN ACCESS
74 REN PROJECTION SUBROUTINE BY *GOSUB 90.* ALL SCALING
74 REN AND PLOT CONTROL NUST BE DONE IN CALLING PROGRAN.

78 REN VARIABLES (XO.YO.Zf). HATR1CE8 T,P,I HIST NOT BE
80 REN NODI PI ED BY CALLING PROGRAM. LINE NUMBERS IN

82 REN CALLING PROGRAM SHOULD BEGIN AT 100.

84 RETURN

Lines 10 through 42 in the progran acconplish the input of the observation point and
conputation of the transf ornation natrix T. Line 44 is an unconditional transfer to the first
statenent of the calling progran which generates the points to be projected. Dote that this
requires that the first line in the calling progran be 100. Lines 50 through 82 carry out the
conputation of the intercept point (designated by , 12 , and 13). sod the natrix projection
of this point fron e3 into E2 .. This subroutine is accessed fron the calling progran by GOSUB
50. The return t.o the calling progran is in line 84. The result is the generation of a projected
point (P^ ,P2> corresponding to each object point (x,y,z). This projected point can be scaled
and sent to a graphic display device such as an XT plotter or cathode ray tube. All scaling and
plot control nust be handled in the calling progran.

401

Id this section, several applications of the perspective projection algorithm will be
presented- The examples have been chosen to show different and unusual graphic representations,
and to give a feeling for the power of the algorithm.

Figure 3 - Sphere

Figure 3 shows a sphere of unit radius centered on the origin as viewed from the point
(2,2,2). Latitude and longitude lines have been drawn every 1^/12 radians. Students often have
difficulty visualizing a spherical coordinate system. However, an exercise to produce a drawing
of this type has been found to be of great value. The program to produce the drawing (as well as
the programs for the other examples) is in the appendix.

4 C»

Figure 4 - Fourier Synthesis of Square Wave

The Fourier synthesis of a square wave furnishes an interesting application for the
projection algorithm Figure 4 shows a drawing of such a synthesis as viewed froa (5#-ci#8), The
square wave has a wavelength of 4. The first line in the drawing shows the first tern in the
Fourier series. Pjch subsequent line represents an additional tera added to the series.

Figure 5 illustrates the potential field associated with an electric dipole. The charges
are located below the plane in which the potential is conputed to avoid the problea of infinite
potentials. This exaiple shows very clearly the perspective characteristic of the projection.

'The observation point is (-15,15*10).

Figure 5 - Potential Field

ERIC

403

Displacement

Distance

Figure 6 - Traveling Have

A traveling wave with unit amplitude as viewed from (10,7,10) is shown in Figure 6, As tine
increases, the wave clearly loves to the right. Also, the drawing nates obvious the point that
lines of constant tine as well as lines of constant distance are sinusoids. This type of drawing
can be used to illustrate the notion of wave velocity to great advantage*

Any of the drawings can be converted to stereo pairs b. Baking an additional drawing with
observation point chosen such that the new line of sight Bakes an angle of about 10 degrees with
the old line of sight. If the two drawings are then viewed through a stereoscope, very
interesting effects can be obtained. Students particularly seen to enjoy this type of exercise.

The programs utilized to generate the eibftples are contained in the appendix. While these
programs are in BASIC, the structure of the algorithm is clear and it could be done equally well
in any computer language. The prograas in the appendix only generate a set of points (x,y,z)
which then Bust be projected. Thus, the prograa in Figure 2 Bust be added at the beginning of
each of the exanpie prograas.

The drawings in this paper were prepared on a Hewlett Packard 9100 XT plotter using a tape
generated on Hewlett Packard 2007 Educational Computer System. The programs can be converted to
an on-line Bode by: deleting all CALL(1) statements, replace CALL (3) stateaents by PBINT
"PLTL", replace CALL (2, A ( 1) , 2) stateaents with PRINT (A(1)#A(2), and replace CALL (5) statements
with PRINT "PLTT."

The graphical techniques described in this paper have been used successfully with lower
division students in physics and aatheaatics courses. Students can be taught to work in graphic
projections whether they understand the nathematics of the projection or not. There are
compelling reasons to get students involved in graphics if at all possible. Ideas which nay be
difficult to transmit emerge with clarity if approached graphically. It has also been observed
that when students write programs to produce graphical representations they become completely
submerged in the problem. This leads to a depth of understanding that is difficult to obtain by
other nethods.

Saaslaaifiii

404

APPENDIX

Program For Sphere

100 REM SPHERE
lie LET 81 sSiff
120 LET 0S3.I4I59
150 CALL (1)

140 TOR A*0/12 TO 11*0/12 STEF 0/12
150 CALL (5)

160 TOR B*0 TO 2.01*0 STE0 0/12
170 LET X:SIN(A)*COS<B)

180 LET YsS10(A)*SlN(B)

190 LET Z:C08(A)

200 B06UB 500
210 NEXT B
220 CALL (5)

225 NEXT A

250 FOR Bs0 TO 2.01*0 STE0 0/12
240 CALL (5)

250 FOR As# TO 1.01*0 STE0 0/|2
280 LET XsSIN(A)*COS(B)

270 LIT Ys81N(A)*81N(B)

280 LET ZzCOS(A)

290 QOSUB 500
500 NEXT A
510 CALL (5)

320 NEXT B
350 CALL (1)

540 8TO0

500 REH 0LOT SUBROUTINE
510 00 SUB 50

520 LET All IsSNTCSl *011 Jf 5000)

550 LET A(21:INT(S1*0(2 H5000)

540 CALL (2.AN 1.2)

550 REH END SUBROUTINE
560 RETURN
999 END

Program For Fourier Synthesis Of Square Wave

100 REH FOURIER SYNTHESIS
110 LET SI sf 500
120 LET 0S3.14159
150 CALL (1)

140 FOR Nsl TO 10
150 CALL (3)

160 FOR X:0 TO 4 STEF 4. 00 000 E- 02

170 LET Z=0

180 FOR Hsl TO N

190 LET ZzZ+S!N((2*n»l )*P*X/2)/(2*N*l)

200 NEXT H
210 LET Z:Z*4/0
220 LET Ys2*N/10
230 SO SUB 400
240 NEXT X
250 CALL (5)

260 NEXT N
270 CALL (1)

280 STO0

400 REH 0LOT SUBROUTINE
410 GOSUB 50

420 LET All ):INT(S1*0(1 H2000)

450 LET A(2J:INT(S1*0(2)»5000>

440 CALL (2. All 1,2)

450 REN END SUBROUTINE
460 RETURN
999 END

4CS

405

Program For Potential Field

LIST IM

IM REN POTENTIAL FIELD IR XT FLARE.

IRI REN FRON URIT POSITIVE CHARGE AT <9,0,-9»
IS2 REN AND WIT SEDATIVE CHAROE AT <-9,0,-9>
IIS Ln SI *200
12# Ln S2S2R
130 CALL <|>

I AS FDR X*-I0 TO I#

190 CALL (3)

l<« FOR Y*-I0 TO I#

I7S Ln El *1 /S0R<<X»9> f2+Yft+29)

IS* Ln 22s*l/S0R((X»9>1t4Yt8At9)

I9S UT Z*SB*<ZI*Z2>

2ft 30 SUB 9#

21 • Ln A(l ]*INT<£l*Pd H9000)

22S Ln A (2 1*INT<S1*P!2 1*9000)

23f CALL (2»Ad l#2)

240 NEXT Y
290 CALL (9)

260 NEXT X

270 FOR Y*-10 TO 10

280 CALL <3)

290 FOR Xs-10 TO 10

300 LIT Zl s|/SGR((X*9) f2+Yf2+29)

310 UT Z2*-l/S0R<<X+9>«2+Yt2*29>

320 Ln Z:S2*<ZI*Z2>

330 30 SUB 90

340 Ln Ad )*INT<St*Pd H9000)

390 Ltt A(2I*INT(SI*F(2 K9000)

3S0 CALL <2, Ad 1,2)

370 NEXT X
360 CALL (9)

396 NEXT Y
400 CALL d>

999 END

Program For Traveling Wave

100 REN TRAVELING WAVE
110 Ln SI =790
120 LET PsS.14199
130 CALL (I)

140 FOR X* TO 2.0I*P STEF P/6
190 CALL (3)

100 FOR Y*0 TO 2.0I*P STEP 2*P/90
170 UT ZsCOS(X-Y)

180 OOSUB 900
190 NEXT Y
200 CALL (9)

210 NEXT X

220 FOR Y« TO 2.01*P STEP P/6
230 <i*|| (3)

240 FDR X*0 TO 2.01*P STEP 2*P/90
290 UT ZsCOS(X-Y)

260 OOSUB 900
270 NEXT X
280 CALL (9)

290 NEXT Y
300 CALL (3)

310 UT Y*Z=0
320 FOR XW TO 7
330 OOSUB 900
340 NEXT X
390 CALL (9)

300 CALL (3)

370 UT X*Z*0
380 FOR Y* TO 7
390 OOSUB 900

400 nxr Y
41# CALL <9>

419 MU C3>

4*0 LET X*Y*0

430 por nr yd a

440 BOMB 900

490 NEXT Z
400 CALL (9)

470 CALL (l>

480 STOP

900 AIM PLOT 8UBR0UTINE
910 808UB 90

9B0 LET All )sINT(8l«PU H4000)
980 LIT Alt !c!BT<8l«P(B|» 7000)
940 CALL <8,AIIlt£>

990 RfH BD SUBROUTINE
900 RETURN
999 BD

►

407

CONPUTER GRAPHICS AND PHYSICS TEACHING

Alfred H. Bor A and Richard Ballard
University of California, Irviae
Irvine, California, 92664
Telephone: (714) 033-6911

Last year at the Dartmouth Con ference ( 1 ] we reported on the Physics Computer Development
Project's use of computers in learning physics. He are concerned with procedures and areas in
which the computer gives leverage in teaching difficult to obtain any other way. Our work has
encompassed all modes of computer usage: dialog, computation, and simulation. Furthermore we
have worked with full classes, testing our material with 150 students and rewriting it based on
computer-saved feedback.

Our early work was with character-oriented terminals, either hardcopy or softcopy[2].
However, from the beginning we were interested in using graphic terminals; and recently our
software development has permitted us to implement and use graphic teaching material for physics
courses. This paper describes the types of usage of graphics in teaching we are exploring and
the underlying software for graphics.

Pictures jn Teaching

By looking in any textbook or visiting any lecture we can see that pictures, diagrams, and
graphs are useful in teaching. The crude ability of alphanumeric terminals to present graphics
has often been invoked in educational situations. Even a terminal such as the Hodel 33 Teletype
can simulate point graphs by typing characters in fixed positions. Some of our dialogs produced
crude diagrams and students often tried to graph output from their own programs.

Graphics in a timesharing environment has been expensive. However, new terminals and
spectacular decreases in price promise that graphics will soon be widely available for students.
These terminals can, under computer command, draw a line from one point to another on the screen
and thus draw pictures of arbitrary complexity. Little use has been made of graphics with live
students, so little is known about its effectiveness in teaching environments.

It is convenient to distinguish two types of computer usage in teaching, one in which the
student writes his own programs and another in which the student interacts with existing
programs. Implementation of graphic facilities is different in these two cases, and perhaps they
even have different educational values.

Host of the work described here deals with this last type of usage. He will look first at
the underlying graphic software used in dialog programs, then at comparisons of popular dialog
programs which exist in both graphic and nongraphic forms. He next look at dialogs in which
graphics is the key element. flOTION, a program for exploring classical mechanics, is given
special attention. At the end of this paper we discuss briefly an interesting possibility for
graphics within student written programs. As of this writing, the graphic software for this use
is in early stages of implementation.

Underlying Graphic Software for Dialogs

Our development of graphic software was an extension, within the same tradition, of our
software for generating student -computer dialogs without graphics. Our approach has been to
write assembly language macros which access assembly language subroutines. As teaching needs
develop, we write new macros; so graphic teaching is a special case for our general tactic(3]«
He make no attempt to give a complete software description; full documentation exists for those
interested [4] • He illustrate some of the principal graphic macros, available under the BTA and
UTS timesharing systems on the Xerox Sigma 7.

Graphic data can be computed within the program or fixed drawings can be part of the
program. Typically in our programs the data is computed in code which originated as FORTRAN
subroutines. The graphic data from the subroutine is in arrays.

The teacher night first decide where the picture is to appear on the screen. He might want
to put several curves on at one time and to nix graphic with alphanumeric material. So the
teacher needs an easy way of controlling where things appear. (In practice this is complicated
by the fact that screens have different sizes and orientations; although our software covers
this, we will not discuss it).

He let the user specify where he wants the curve drawn by a HINDOH command with
specifications in inches from the lower left hand corner. Suppose, for example, that he wants a

4CS

409

curve, perhaps one of several, to appear in the box or window illustrated in the following
diaqran;

The statement within the prograa to establish this window would be:

U*DOU (5,2) , (7,4)

The user can also specify a box
around the window if he so desires:

WIRDOW (5,2), (7,4) , BOX

■or sally the box will not be drawn.

The teacher aust next decide «k&££ within the window the curve is to be. Possibilities are
nuserous: we can choose to have the x and y or x, y and z data scaled so that it occupies the
full window* or the origin of the coordinate systea can appear at the center of the window. Or
the teacher nay specify the coordinates of the ends of the window, again in two or three
diaensions. The following uses of the aacro SCALE let the user assign coordinates to the window:

SCALE (XI, 12) , (II, T2)

SCALE (P.Q) ,<X,T) , (A, B)

P 6 Q are the ainiaua and aaxiaua
for the first variable plotted,

X 5 t for the second, and
A & B for the third.

After establishing the window and the scale, we next draw the curve. The data will be in
two or three arrays; the FORTRAtf routine also returns us the nunber of points to be plotted. The
connand CURVE connects each of the "points" in the arrays with straight line segaents. If the
curve is three-diaensidnal, it is projected onto the two-diaensional screen.

Typical uses of the CURVE connand are as follows:

CUIVE

2-D

plot

CURVE

(HOB, VER, OUT, H)

3-D

plot

CURVE

(RAX. (X.r.H))

3-D

plot, curve is scaled to touch window

*09

410

cuavs

on all sides.

(CENTER, ( AA,BB,CC ») ) (o,o) is centered in t^e window.

The fourth command, the 1st we describe in detail, is AXES, drawing axes for two or three
dimensional curves. Here are soee examples:

(DIE, 3)

2- D axes using current scaling data

3- D axes

(hAX, ( A , B, SO) ) , LIHITS
Axes for largest possible
curve. Haximum and minimum values
of axes are shown.

(LABELS , 1 X1 , • Y1 )

(LABELS, •VX,,,VYf#*VE#)

Other macros are needed for positioning the beam, for erasure, and for specifying the
graphic terminal; current software supports the ARDS 100, the Tektronix 4002, the Tektronix

4002A, and the Tektronix 4010. Adding a new terminal is a simple modification. A graphic program

starts by asking the s indent which type of terminal he is using; with present terminals,

unfortunately, the computer has no way of knowing the nature of the terminal. (He have

information available [5] , for those interested in the problem, about terminals for an
educational environment.)

Graphic and Nongraphic

Several dialogs which use graphics are available in both graphic and nongraphic form; this
gj-'es us tie opportunity to comment on the effectiveness of graphics. If a program exists in
both forms, we would not expect it to be the same program, because the availability of new
facilities indicates different possibilities in the teaching environment. Particularly in the
early period of understanding the use and effect of graphics in learning it is valuable to have
some similar programs attempting to exploit both graphic and nongraphic environments.

One dialog in both forms is the widely available one-dimensional lunar landing simulation.
He have a nongraphic version, with numbers coming out., plotting the position in the usual
typewriter way. This was written for our system by Noah Sheruan and Steven Derenzo at the
Lawrence Hall of Science, University of California, Berkeley.

The graphics lunar landing simulates a stylized spacecraft panel, with the position,
velocity, and fuel indicated on graphs or gauges. The "instr uments" are changed when the pilot
gets close to the lunar surface, so th^L the student can get a more detailed view.

Both versions are popular with students; this is our most widely used program, both with
physics students and others. It is clear from observing students that physics talent needed in
one program differs from that needed in the other. In the “numbers" program, without graphic
output, good students make " 1/2 at2 " calculations to determine fuel requirements in the final
stages of landing; it was in connection with getting experience with the relations involving
motion at constant acceleration that the dialog was developed. The graphics dialog makes
students rely on curves of position and velocity vs. time and so has an entirely different
MfeelM to it. Students no longer make calculations but must develop an intuitive idea of what it
is like to be involved in a constant acceleration environment with some fuel to slow down. He
suspect, although we could not prove, that students learn more in the graphic environment in
developing an intuitive feeling for the laws of motion. He contemplate tests involving those two
ver sions.

A second dialog available in both graphic and non-graphic forms was developed by Hurray
Alexander of De Anza College in Cupertino, California. It is a "race", the Permatopolis 500. In
this somewhat unusual race the drivers have no control over the speed in the two laps. They go
from (0,0) to (500,500) as shoun in the following diagram:

(500* 500)

(500,250)

410

A change in speed occurs only at y = 250. The speeds are announced in advance for each race
for each of the tun areas, and are the saae for both "drivers.* Each driver picks x
corresponding to y = 250. The object is to win the race by keeping the tine of travel as short
as possible. The physicist sees that a minimal principle is involved, Fermat's principle in
optics and leading to Hamilton's principle in mechanics. Variational principles are certainly an
important way to formulate physical laws. Here is an important physical idea, vital in
contemporary physics, almost totally oeglected in the vast majority of introductory courses.
Hence the computer has an opportunity to contribute significantly to learning in physics^ Even a
professional quickly discovers he is better off using his intuition than attempting to make the
calculation, and the nonprofessional quickly sees what is involved in finding a minimum time in
such a situation. The reward systea has a higher payoff if the student's time is closer to the
aini .tun; winning or losing depends on several races, with different speeds in the two regions.

With PERM it is lore difficult to be definite about the advantages and disadvantages of the
graphic versus the nongraphic form. In the graphic form you see the race happening, while in the
nongraphic version you see only the resulting times; we believe that you get some feel as to why
you win in the graphic version, because you observe that the winning person travels farther in
the faster regi j So there seems to be a gain in the graphics, but perhaps this gain is not
sizaole. Again we intend to do some testing with students using both versions, to see which form
more quickly develops the students' intuitive understanding of action principles. We hope too to
develop increasingly complex follow-up games of the same type, further extending the notion of
variational principles.

GRAPH performs a utility function for s-.udents, one that we feel is very valuable for
physics classes. As its name indicates, it graphs functions Students should do some graphing by
hand, but it is difficult to generate large numbers of graphs by hand. Vet seeing relations
graphically is often an important part of understanding the physical aspects of a mathematical
result. GRAPH makes it possible to examine many curves concurrently. Students enter the function
in the usual notation with relatively few restrictions. The program contains its own parser
which analyzes the functions and generate the graphic data. Students can request many
different plots, set constants in equations to different values, etc. Functions are in
parametric form, and plotting in tuo and three dimensions is available as in all of our graphic
mat er ial.

This program has also found a use entirely different from that initially intended, in a
"physics for artists'1 class. If we connect points on a curve which are not close together, we
can construct beautiful patterns. The program allows students to control all variables,
including the time step between successive points to be plotted.

MOTION is a more elaborate instructional program using the computation, language
recognition, and graphic facilities of the computer. In combination they have produced an
exciting new tool and introduced several new teaching strategies.

MOTION was written to aid students and instructors at all levels in a study of equations of
motion. The program offers each user a large repertoire of motions* Choices range from simple
harmonic, centra' force, and constant acceleration to che very uncommon motions associated with
two force centers or a multipole field. One can view the effects of anharmonicity , uniform
electric and magnetic fields, or even the scattering from a nuclear force. A revised version
will usA parsing routines permitting students to write their own equations of motion.

Classical mechanics offers unique opportunities for using the computer to carry us far
beyond present course boundaries. We have had ample demonstrations here and elsewhere that
simple numerical methods, like the Euler method, can be taught to students at every level [8]. It
is difficult to overstate the potential significance of introducing students so early to so
powerful a tool. The beginning student can tackle problems and physical systems heretofore
reserved to graduate student...

We are only just beginning to exploit the opportunities that a numerical approach provides.
We have developed considerable experience in using these methods with large classes of
students [1]. We have probed many of the pedagogical barriers to a wider use of computers. MOTION
was written to overcome what seemed the more serious of these probleas.

Perhaps the dominant objection to numerical solutions is that they produce a numerical
result. For the most part it is difficult to interpret such results- to extract their physical
consequences and go on to anticipate the solutions of other problems.

Wheeler proclaims as hs First Moral Principle [9] , "Never make a calculation until you know
the answer." Tor many of our students, development of a physical intuition and an appreciation
for the range of physical phenomena will serve them better than a knowledge of the mechanics for
producing a particular solution.

412

With numerical solutions all results appear the saae on the teletype, simple coluins o f
numbers. Students rightly balk when asked to translate these nuibers into graphs- They often
view the process of changing parameters and replotting as tiresome busy work, yet repetitious
plotting is the k^y element in learning from numerical solutions.

✓

ERJC

IUH2RBZS33 ■

Using MOTION

NOTION uses a graphic dialog approach to overcome this objection- Students acquainted with
the underlying algorithm can use that knowledge to explore the sensitivity of solutions to time
step and other considerations. Other asev s, knowing nothing of such matters, wi'l never
encounter them. Using simple English they can choose motions for study, change constants and
initial conditions, and then observe consequences of such changes.

The program can provide a fora of instant experience to the student. In a very short time
he can develop a gualitative understanding, for example, of an£ central force described by a
power law or the sometimes spectacular orbits of a planet in a binary star system. The student
is not restricted to plotting only spatial variables, nor in the choice of two-and three-
dimensional projections. Virtually any physically meaningful variables can be plotted against
any one or two other variables.

The explorative characteristics of an instructional program like MOTION are very important.
Students bring to their physics classes a very narrow range of experience. While this has always
been true, it has become increasingly acute as physics moves on to microscopic and macroscopic
levels far removed from everyday observation- Students need this experience to understand
physical principles- Great laws only appear as such when they help us to consolidate a variety
of seemingly unrelated observations. MOTION offers a rich universe of examples. The unique
behavior of total energy is nowhere more impressive than in three body motion. Its straight line
time dependence stands out strikingly against the bizzare trajectories traced by other
variables. We provide a wide range of physical examples, some obvious in their conservation of
energy and in momentum, some not.

The sense of exploration in MOTION is quite real- If one ignores the infinity of variations
produced by changing initial conditions and equation constants, over a hundred and fifty
thousand distinctly different combinations of equations and variable projections are possible.
Most of these have never been seen before by anyone. As a consequence, eygr y user has the
opportunity to learn something new and make genuine discoveries- Unlike most instructional
programs, both the instructor and the student users are offered an opportunity to learn. If
anything, the instructor's knowledge and experience may permit him to learn even more than the
student. This last aspect has been exceedingly important in gaining faculty acceptance for the
program. Instructors can test the effectiveness of the program on themselves.

Response Recognition in HOTION

Explorative programs like MOTION are difficult to program. The bulk of the computation and
display options are straightforward; the tricky question is how to educate the user in the
existence and operation of so vast a collection of options: all the equations, variables,
projections, scaling, families, 3-D aids- like rotation and dashing. We chose a dialog strategy
that puts the student in control of the program flow, letting him call for the facilities he
wants. We take full advantage of dialog technique as a means of producing stand alone programs.
It requires no prior instruction or descriptive handouts and adapts to the terminology and
abilities of an enormous range of users.

MOTION attempts to recognize anx question or request relating to its functions of
selecting, solving, displaying motion. Although this sounds to be most difficult, it is not an
impossible task. It departs completely from the patterns of program flow found in computer
dialogs on programmed instruction. Students accustomed to these conventional dialogs will
sometimes ask, "Where am I in the program? What can I do next?" The answer is that despite
appearances they are always at the same point and that they are free to try anything they want.

Each input is inserted into a rinq which performs an exhaustive search for key word
fragments or symbols- As successive requests or questions are often related, the search process
is made most efficient by inserting the input adjacent to the last successful key match. Suppose
the student’s last input was recognized as assigning a new value to one of the initial
conditions. He is more likely to change another or to ask for a "plot" than to request another
equation of motion. The program will do either, but checks first for the most logically related.

Once the presence of one or more key word fragments or symbols has been detected,
subroutines are called to break down the message syntax. If parts are missing, the program
requests their entry- Here again we try to avoid any "flow traps-" We look first fcr the missing

413 *

4.12

information; if not present, we reinsert the new input into tho test ring, on the chance that
the user has disregarded our question and changed the subject.

These recognition facilities have proven quite effective. Anyone who knows what he wants,
can ash for it. If clearly stated, he will usually get it. He need change only those things he
wishes changed; all others will renain the sane. If he does not set equation constants or
initial conditions before asking for a plot, the progran loads in an interesting example and
proceeds to plot it.

MOTION employs several techniques for enlarging the student's knowledge of its facilities.
The imaginative user will ask questions. This does not come easily; many users put off "wasting
their time" until a high level of responsi veness has been demonstrated. Some reject the notion
entirely. This may be the result of a previous exposure to computers; the totally uninitiated
often accept the idea with great glee and begin asking questions having little relationship to

questions are usually answered with an excess of information. The requested facility is
described and notice is taken of other related facilities perhaps unknown to the user.

Students having trouble with the program are also given an opportunity to learn. Whenever
an input cannot be recognized, failing all tests, the program randomly selects a message
appropriate to that area of the program. It describes some of the available features, using
quotes to emphasize recognized terminology.

Observations on student Use of MOTION

MOTION has been used by a spectrum of students, instructors, and computer professionals. It
is, first of all, highly popular. Left to themselves, many students have spent the better part
of a day running the program and return frequently thereafter. It was immediately adopted,
highly recommended, and heavily used in the upper division mechanics course. Previously, the
instructor had seen little use for computers in teaching. We are now testing the program with
large classes at the introductory level.

The ways of using MOTION are varied. Instructors could connect the graphic terminal to a
scan-converter and use the program as a televised demonstration in lectures. The format free,
natural language approach in communications makes it very easy for instructors to learn its use;
the absence of flow keeps then from wasting class time, if an error is made.

It is most often used by students as an adjunctive aid, available at any time. Students
move easily between physical systems and discover quickly both two- and three-dimensional
projections. Their reaction to the variety of variables that can be plotted seems to depend upon
their educational level. The beginning student looks only at plots of position and time
coordinates. The odds are against his discovering anything about energy conservation, momentum,
angular momentum or motion in phase space until he has received some formal instruction. Our
observations seems supportive of Bunderson9s findings that directed instruction is more
efficient than a pure discovery approach for the average or below average student [9]. In its
present form MOTION serves these students by offering then a universe of dissimilar motions in
which to test their newly learned abstractions.

G ca phics ig Student Programming

Our computer usage with students has involved students interacting with canned programs
such as those just described, graphic and non-graphic, and it has also demanded that students
write their own programs for solving physics problems. In the beginning course the two usages
are about equal; in both cases comments of students at the end of the course suggest that we are
at a reasonable level with regard to the amount of usage, although our students "vote" more
favorably for dialogs than for computation. The total computer usage in the beginning course is
about an hour and a half a student each week.

As of this writing we provide no graphic facilities which average students can use in their
own programs. Knowledgable students cou}d use our general graphic software, but this demands
more knowledge than we can reasonably expect from many beginning physics students. Many students
resort to character-type plotting.

Data to be graphed in physics programs is primarily array data. X and I or X and T and Z
coordinates are calculated for many, many points, and then the resulting arrays are converted
into lines on the screen. Using graphics naturally within a student-written program depends on
the ability of the programming language to conveniently construct and manipulate arrays of data.
Two existing interactive graphics systems, the Culler-Pried and the Harvard TACT systems, both

the program.

Figure 1

¥T

Figure 1: Inverse square force, varying initial velocity

Figure 2: Inverse square force, velocity space, varying initial velocity

Figure 3: Inverse square force, kinetic and potential energy as functions of tine

4:14

languages.

oriented toward easy Manipulation of graphic Material are also array-oriented
However, these specialized languages are available in only very few places.

Of the connon general purpose languages we night use with physics students, the one
presenting the best array capabilities and therefore the one nost suitable for graphics is APL.
API has other advantages as an introductory language for students, Mating it the language of
choice if all current languages were available in a given location [ 1 0) .

Since API can use array argunents to functions, several natural ways for graphics are
available. Sone eiper inentat ion with running systens will be useful for deternining which of
these is both nost natural for the experienced aPL user and easiest to Manipulate for the
beginning user. If A and B are arrays of the sane length containing the data the following API
connand, for exanple, night generate the graph:

DBAW A VS B

Just as in dialog graphics, we need windowing and scaling, so additional functions are also
necessary. And 3-0 graphing should also be allowed[11].

He hope to have a running APL graphic systen soon, so we can gather experience with
students. In generating teaching Material we believe it essential to interact at all stages with
students and to adapt the fora and structure in ways that are anenable to then, rather than
forcing then to natch the software.

Conclusion

He have reported on graphic developaent and plans within th£ Physics Coaputer
Developnent Project. Sone of the ways outlined are dependent on the physics teaching Material,
so other areas nay find other nodes aore natural. It nay turn out that graphics are not nore
effective than cheaper aethods of coaputer output in sone areas. He believe that in physics the
case for graphics is already strong and we believe that the potentialities for the future are
great* He encourage others to~experiaent both within physics and in other areas to learn the
capabilities of graphic teaching Materials.

BEPEBEH CBS

1. Boric, A., The Coaputer in a Responsive ^earning Bnyjf oane Let a Jhousand Flowers Bloon.

2. Bork, A* and Ballard, B., Jhe Physics Cjgnputg* Development PrQi^ct.

3. Boric, A. and Nosnann, C. , Teaching Conversations with the XP5 Sjgia 7-- Systen Description.

Mosnann, C. and Boric, A*, Teaching Conversations w jtfr tfre jDS Sjgna 7 — SYStea Usejs

Warner, E- and Boric, A., Teaching Conversations wjth the IDS Signa 7 — Systen Maintenance
Manual.

4. Bork, a* § Warner, e. , and Collins, J*, Teaching Conversation wjLt£ the XD§ Sicja 7 — Graphic
Dialog Facilities.

5. Bork, A., Terninals for Education^

6. Bork, A., Inexpensive Tineshared Graphics wjtb the Sjgna 7.

7. Bork, A., Luehrnann, A. and Bobson, J. , Introductory Cqnpu tqr- Based Mechanics.

8. Taylor, E. and Wheeler, Jr., Spacetine Physics.

9. Bunderson, c. , instructional Software Engineering.

10. Bork A., Science Teaching and coaputer Languages.

11. Bork, A., Graphics jn ft EL.

416

STATISTICAL PHYSICS COtfPUTER APPLICATIONS

Harold Weinstock

Illinois Institute of Technology
Chicago, Illinois 60616

Introduction

Statistical mechanics is a
areas of physics specialization,
difficult for students to master
only a select number of sometime
nations or even homework). Tla
and aeaningful problems.

subject which is of fundamental importance in a great variety of
Yet, it embodies a number of abstract concepts which prove
, and because of calculational complexities or time limitations,
s unrealistic and trivial problems can be assigned (for exami-
coaputer can be most helpful in broadening the range of solvable

While this last statement may be made with validity about most areas of physical science,
it is particularly appropriate for statistical mechanics. This subject involves calculation of
macroscopic thermodynamic parameters by taking suitable averages over a large collection of
microscopic entities which comprise a system. Inasmuch as the fundamental postulate of
statistical mechanics states that a system in equilibrium may, with equal probability, be in any
of the physical states accessible to it, a number of computer simulations can be made which will
provide accurate representations of actual physical systems. The use of random number generation
figures prominently in such simulation. The "n umber-crunching M capability of the computer is, of
course utilized both in simulations and in the evaluation of complex mathematical relations.

senio
cla ss
ass lg
wou Id
the in
invol
sol ut
of 3
whom
and
stu de
"Cinn
res ul
resul

In tnis paper I wish to report on two homework assignments I have made to students in
r and graduate level courses. These are assignments which were made after I had motivated
discussions on hopefully meaningful problems not normally handled. While each of these
nments could have been completed without the aid of a computer, in one case the computation
have been prohibitively time consuming, and in the other case, most students did not have
at hematical sophistication and intuition to solve the problem. However, both assignments
ved elementary programming skill and required a relatively limited amount of time to find
ions. All (15) students involved were able to complete these assignments with some measure
uccess. These students ranged from junior class physics majors to graduate students, all of
had previously been exposad to at least one introductory programming course. The programs
output to be presented below represent upgraded versions of some of their efforts. Por
nts in an introductory physics course, this material could be used in subroutine or
ed" form. An interesting fact about both these problems is that the students found the

ts unexpected in almost all cases considered, while even I uas
ts.

startled by some of the

3na Dimensional Random W&lk with Unequal Probabilities

As an
random walk
events by a

introduction to statistical fluctuations and distributions, the
problem is generally presented. It is observed that one can describe
binomial distribution of the form:

one dimensional
such a chain of

pn(N)

M! n (N-n)

(N-n) !n! ^ q

where PnW is the probability of moving n positive, e.g., right, steps in a total number of
trials (or steps) N;p is the probability of moving in the positive, e.g., right, direction for a
given trial; q is the probability of moving in the negative, e.g., left, direction for a given
trial; and p ♦ g -• 1 for all possible situations for which the distribution applies.

The usual example given involves a drunk starting out at some origin and (unrealistically)
moving randomly either forward or backward with equal probability ( p =g = 1/2) in taking steps
of equal length along a straight line path. For a given total number of steps N, it is easy to
use the above equation to calculate each Pn(N) and arrive at the symmetric discrete binomial
distribution in which the most probable position is at the origin, assuming N is an even number.
This result seems to appeal to everyone’s intuition and is expected.

Rarely, however, are
investigated even though, as
with regard to the motion of

the consequences
it turns out, its
wave packets.

of a non-symuetric, p / q,
consequences are unexpected

binomial
and have

distribution

significance

4;.'g

417

To remedy this situation, I challenged ay class to tell art where I should place the drunk
in a linear sequence of 31 squares, nuiber 0 to 30, such that he *ould arrive safely at either
the 0 or 30 square with equal probability when p * 2/3 and q = 1/3. As expected, the class
unanimously agreed that square 10 should be the correct starting position, i.o., that position
which divides the total nuaber o.; squares into two segments whose ratio is that of p/1. Rather
than take advantage of the student's naivett in playing a related game based on ay having the p
- 2/3 probability of a successful trial, I presented them with the following problem:

0 12

“Assuming a random distribution of independent events with p = 1/3, q = 2/J; a field of play
yith 31 positions labeled consac u tivel y foa 0 to 30; a move of one unit to the left with a ‘p‘
result and vice versa fro a ‘g* result; a win for you when the zero position is reached; and a
vin for me when the 30 position is reached; what nuaber should you designate as the starting
position to make the gaae fair? Solve this problem using standard mathematical techniques and do
a simulation of it on the computer ‘playing* at least 10 ‘games* at the position you think (or
have found) to be the fairest. h

A11 of the students in tha class were able to do the programming necessary to carry out the
assignment although the degree of sophistication varied* Yet, only two of them were able to
solve the problem by standard techniques using a recursive rela t i onsh i p[ 1 ]. Even then the
solution was not in closed form as it required the entry of that starting position which would
produce an equality or near equality. Thus, the computer simulation was useful in providing the
correct region for tne starting position, if not in fact the correct answer by virtue of a
sufficiently large number of simulations.

To dispel any lingering curiosity about the outcome, let me point out that the fairest
starting value is found (both mathematically and by simulation) to be position 1. Starting at
that point, the probability of reaching position 30 is just a bit greater than 1/2. For example,
in one hundred trials a student found 52 trials which ended at 30.

Figure 1 illustrates a convenient form of output for this problem. Snown are the random
numbers generated by the computer and the resulting position (of the drunk) for a given starting
position. The students soon realize that with a starting position of 1, their chances of success
in the game, i.e., reachiny position 0, diminish rapidly if the initial step is in the positive
direction. To keep the total output down to a reasonable size, only the first ten games in a
sequence of 100 tor a given starting position are plotted. Then a summary of wins for each side
is given.

Although this exercise was introduced within the context of a statistical mechanics course,
I believe it is just as significant as an illustration or the statistical foundation of quantum
mechanics. The non-symme t rical binomial distribution can be considered as c ha rac ter istic of the
behavior of a particle acting under the influence of a uniform force field while subject to
random collisions. For example, this situation would apply to a charged particle in a gas acted
upon by an electric field. It can be said that while the most probable position of a particle
moves in the direction dictated by the applied force field, its wave function spreads out in
space. Thus, there is always a non-zero probability that the particle will have moved in the
opposite direction. This probability diminishes rapidly once there has already been some
“drift*1 in the opposite direction.

The programming skills required to perform the above descrioed simulation is elementary and
well within the capability of in upperclass physics major or graduate student. A flow chart of
the proyram used by the author is presented in Appendix A.

Heat Ca^ac it y f 21 Systems

A fairly standard problem is one which involves calculation of the heat capacity of a
system of N classical particles with atomic spin S = 1/2. Quantum mechanical considerations,
which must be applied, dictate that there are only two energy states available to each particle
(corresponding to oppositely directed spin orientations). Calculation of the total energy of tne
spin system, and subsequently its heat capacity is straightforward and simple. The average total
energy of the system (E) is determined using the general expression

, where e. = the energy of the i — level,

= the degeneracy factor of the i— level
and (S = 1/kT.

E = N

l e,g,e”^ei
i 11
r -tfe.

?gje i
l 1

418

1 STARTING P0INT
EINSTEIN WINS
GAME MOVES 47

1 STARTING POINT
MEWT0N WINS

GAME MOVES 5

.678

.939

.631

* .590

• 431

.283

* .135

* .237

.647

* .067

• 379

.849

• 335

.609

.615

.191

.727

.847

.319

.552

.517

1 1

.535

.651

.876

.424

.812

.522

• 546

• 416
.667
. 1 64
.403

.685 21
.783 22
•436 23
.467 24
.190 23
.915 24
.684 25
.339 26
.050 25
.533 26
.981 27
•844 26
•522 29
.289 28
.450 29
.162 28
.969 29
.232 28
.726 29
.387 30

NEWTON WON 48 GAMES
EINSTEIN WON 52 GAMES

Fig. 1 - Selected sample output for random walk problem with p = 2/3, q =

1/3.

419

This expression is valid far any system represented by a discrete number of levels- The heat
capacity at constant volume (cv) then is obtained using the fundamental relation

y ieli ing ,

r = -----

v kT2

For a two level system, one rarely bothers using such rigorous formalism to evaluate Cv .
Since the value for Cv depends only on the difference in energy between levels, one can assign a
value of 0 to the lower level and a value of t to the upper one- Equation 1 then becomes[ 2 ]

Differentiating this directly with respect to T gives

('lotting this expression as a function of temperature, shows that at low temperature (kT/e << 1)
the heat capacity rises exponentially- In the vicinity of kT/c = 1/2 it peaks - the so-called
Scnottky anomaly peak - and th an falls off as 1/T2 for higher temperatures (kT/e > 1).

^nile there are numerous physical systems for which t he above discussion applies, there are
obviously '.id n y more wnich are composed of more than two energy levels* As a homework problem I
proposed that my students investigate a three level system (appropriate to many solid state
lasers) ur which the level energies are 0, c, and 3c , and turtner suggested that they present a
computer tabulation and graph of tne resultant cv vs- r. To almost everyone’s surprise, it was
found that there is still only one Schottky peak, again in the vicinity ot KT/c = 1/2, although
there is a quantitative difference between results for a two level system and the particular
three level system cnosen hero-
ine problem of a three level system can be posed in yet another way, one which has
considerable relevance to interpretation of actual physical measurements- Suppose an electron
spin resonance experiment siows two resonances, one at twice the frequency (or energy) of the

otner- Eliminating tne possibility that the higher frequency resonance occurs for a transition

from tne lowest to the highest level, there arc still two possible level configurations, either
0, c, and 3e or 0, 2c, and 3e. Figure 3 shows the graphical output of Cv vs* T for these two

distinct level configurations- Also shown in Figure 2 are results for O-e-^e and 0-4e-5e

configurations- Note that for the 0-e-5c configuration some evidence of a second Schottky peak
is observed.

Tne computer program used to produce Figure 2 and subsequent figures is basically simple
and inexpensive- A flowchart of the program is presented in Appendix 3- Its major function is to
evaluate Equation 3 for the given level configurations- Output is presented in both tabular and
graphical form with up to four level schemes per table and graph. Input includes the level
con f igurat i ons to be evaluated, the temperature interval and whether the levels are equally or
unequally spaced - tne reason for this last piece of information will become evident from a
discussion which follows- if level spacing is not equal, input is limited to 10 levels* If the
converse is true, up to 50 levels may be considered- The ordinate axis is plotted in terns of
the dimensionless parameter Cv/Hk and is scaled from 0 to 1- The abscissa is in terms of the
dimensionless parameter kT/c with the scaling specified by the input.

Another interesting use of this program involves computation of Cv vs* T for a series of
configurations with equal spacing, but with an increasing number of total levels- Pigure J shows
the resulting curves for 2, 5, 10 and 30 equally spaced levels- As one goes from the familiar 2
level Schottky anomaly to the successively higher leveled curves, it is seen that the peak
occurs at nigher temperatures and has a higher Cv/Nk value, and it also is seen that as the

420

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Fig. 2 - Heat capacity vs. temperature for four unequally spaced three level systems:
(0,e,3e); (0,2e,3e); (0,e,5e); and (0,4e,5e).

, ERIC

421

420

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Tig. 3 - Heat capacity vs. temperature for four equally spaced level systems of 2*
5, 10 and 30 levels.

421

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Fig. 4 - Heat capacity vs. temperature for a simple two level system and a similar
system showing hyperfine splitting for doubly degenerate atomic levels.
Note expanded temperature scale.

423

422

nuiber of levels becomes quite large, Cv/Nk approaches 1. Such a result is nothing lore than an
appi^xiaate numerical solution for the heat capacity (tor one dimension) of an Einstein solid,

i.u., a solid in which it is assumed ♦hat each atom vibrates as a harmonic oscillator with a
tixei frequency. There are an infinity of energy levels given by En » (n *■ 1/2)hw, where n nay
be any positive integer. The ground state energy of 1/2 hu (or 1/2 c in the units used here) is
a consequence of quantum mechanics which in no way affects the calculation for bent capacity.
The usual nethod for calculating the Einstein heat capacity[3] is to utilize a mathematical
identity for the sum of an infinite series with geonetric progression. Utilizing a coaputer
generated numerical solution, a student can take a nore active role in arriving at the desired
result and perhaps gains a stronger physical feeling for its significance.

One final application of the program based or Equation 3 is illustrated in Figure 4 for a
two level systea with doubly degenerate levels split by a hyperfine interaction. To siaulate a
physically aeaningful situation, the resulting four levels due to hyperfine interaction are
taken as 0, 0.002 c, c, and 1.002 c. Also evaluated for coaparison is the upsplit (0, c ) two
level systea. o.ie sees that the four level split systea exhibits a nuclear Schottky anoaaly
identical in fora to that observed for a purely atoaic situation. Doth the split and unsplit
systems show the same behavior in the teaperature region of KBT/c^ 1- Students aust be careful
in choosing the scale (sj to be used in handling this problem, as they could easily miss seeing
the nuclear Schottky anomaly and falsely conclude that hyperfine splitting does not aodify the
heat capacity.

REFERENCES

1. See W. Feller, IQ t£2duc t i on £o Probability Th eory and Its Applications (Wiley, New York,
1957) Chapter 14, for a discussion of this problem.

2. For the purposes of this paper, it will be assumed that all levels have the saae
degeneracy, and hence that the degeneracy factor can oe ignored.

3. See F. Keif, fundamentals of Statistical and Thermal Physics (HcGraw-Hi 11 , New York , 1 96b)
p. 254.

)

1 Flow Chart for Random ^alk Problem

P = results in a -1 step
2

Q = — results in a +1 step
Absorbtion limits of 0 and 30

4Z4

425

Flow Chart for Schottky Anomaly Heat Capacity Program

NOTE: Always Maximum of 4 systems with 50 levels/systeir^ and 10 levels/system2

ERIC

426

AN INTEHACTIVE COMPUTER TEACHING DIALOG
FOR SOLVING A SYSTEM OF COUPLED OSCILLATORS

Charles P. Munch

University of California, Irvine 92664
Telephone: (714) 833-6911

ABSTRACT

In this paper the theory and development of an interactive teaching progran is documented.
The efforts extend over a period of one and a half years ana involve usage by a class of
undergraduate science and engineering students. Revision on the basis of student feedback is
emphasized. At the time of the 1972 Atlanta conference, the program will have had a second usage
by the computer based mechanics course.

Computer usage in the physics curriculum at Irvine has been well documented in several
places! 1 , 2 ,3,4] • The Physics Computer Development Project is the primary purveyor of these
applications. Interactive teaching programs or dialogs are a major output of the project. The
purpose of this paper is to report on one of the larger and more involved dialogs that we have
produced. I discuss some of the relevant technical and pedagogical aspects in the production of
such materials.

The program, named COUPOSC, is intended for use with a computer based mechanics course
aimed at science and engineering freshmen. This course was the subject of Alfred Bork's paper at
the previous conference in Dartmouth.

Choosing ^ Topic

One aspect in the production of computer teaching materials that warrants careful
consideration is the choice of topic. Interactive teaching programs are involved and costly
affairs. To maximize effectiveness, we oust consider where the computer will offer the greatest
a dvantage.

The decision to write a program on coupled oscillators was based on several matters. Areas
of the course where students had previously encountered difficulty were examined. The
combination of new mathematical concepts and new conceptual requirements involved in coupled
systems made this a weak area for students. Classroom and text treatments seem insufficient for
many students in developing the notions required for solving problems. In addition, coupled
systems were a transition from mechanics to the study of waves, making the concepts involved
crucial to the students1 progress.

It was felt that the major inadequacy of classroom or text treatments was that the student
was not involved in the derivations. As a passive experience, the student would have more
difficulty in developing the notions than if he interacted directly. Often it is found that even
if a student is able to follow the steps in a derivation, he is unable to reproduce it or, more
importantly, generalize on his own.

With a carefully written dialog, students would be allowed to be instrumental in the
solution of the problem, discovering for themselves what a normal mode was and then being told
its name. With the program offering guidance and remedial help most students could have the
satisfaction and educational advantage of having solved the problem themselves, learning the
concepts as they proceed.

A student having learned this way is at an advantage in solving related problems, in
attempting to generalize from material obtained in a passive situation, a student may find there
are many points where his understanding is insufficient. The reasons behind choices in a
derivation may not be explicitly stated, say in writing the equations of motion or in choosing
the normaL coordinates. For a student who learns by a dialog, his misunderstandings are exposed
and can hopefully be identified by the nature of the responses. In any event, it is felt that
the student should gain a sounder grasp of the material when his exposure has developed as a
function of his thinking.

Int rod uc tion

ERIC

427

The Pe da qoq y of the Interactive Derivation

The idea of

interactive proof originated with a dialog for the derivation of

the
of

so iuch of the style and pedagogy is reflected in the prograa presently being

conservation of energy, docuaented elsewhere [ 4 ) - This author was active in the developnent
that program
discussed.

To give a better idea of how the prograa is structured, a brief flowchart is given in
Pigure One. To ensure that the student has the necessary background, a brief review of spring
forces and siaple harmonic motion is the starting point. The simplest case for the system is
taken. We consider two bodies of equal mass riding in a linear array of spring-body-spring-body-
spring. In the program the notions of degrees of freedom, noraal aodes, normal coordinates,
c harac terist ic frequencies and configuration of the system in a noraal aode are developed.

The objective stated to the student is to find a general description of how the aasses
move. The author's goals can be stated as short and long tera. As a short tera objective, we
wish the student to grasp various concepts- These notions along with soae factual information
comprise the material the student needs at a particular point in the course. What is a more long
range benefit and what can ideally be better realized by a dialog is a skill in handing new and
difficult problems.

If the program is going to realize th
derivation, care must be taken in designing what
asked. In the prograa being discussed, the
decisions relevant to the course of the program a
responses sought from the student range from
formula, to quite general and open ended queries
program is designed so that the student is never
it is requested supplementary information. Freque
the prograa.

e objective of allowing a trul
the student will be shown and what
student is allowed to make all
nd to give all the important
asking for very specific informat
such as "how do we proceed from
presented with long, uninterrupted
nt student interaction is necessar

y interactive
he will be
the important
results- The
ion such as a
here?" The
texts unless
y throughout

One of the easiest ways students become discouraged is when a program fails to recognize
their correct responses. A major effort was devoted to matching sequences that allowed as wide a
variety of correct responses as feasible. Of course, an author cannot anticipate all forms of
correct responses so revision on the basis of student feedback is essential. Revision will be
dealt with in depth later. Matching sequences were structured to allow the student latitude in
the format of the input. Restrictive rules on input format can only be a hinderance in the
educational experience.

At important points in the program where a correct response is not found, extensive
r-.- medial help is available. A student is never told that he is wrong. Depending on the nature of
the question, a student is branched to a number of possible sequences.

In some places, after an unsuccessful match the student is given increasingly specific
hints and is eventually told the answer cr choices he has in how to proceed. In other spots,
where the particular weakness can be identified, the student is taken through a remedial
sequence, usually being asked simpler questions relating to the difficulty encountered. Much
effort is devoted to the recognition of incorrect responses since this allows the author to
respond directly to the particular difficulty the student is having- This recognition sometimes
takes the fora of identification of missing or incorrect elements in the response.

Suggestions and remedial help are given to a student only when responses indicate a need.
Thus, for example, the student having difficulty in the sequence where the equations of motion
are entered can be exposed to several pages of material lasting thirty minutes. A student who
can immediately write down the answer may see six lines and take one minute.

Our system has extensive capabilities for storing and sorting student inputs and these are
used to their full extent in this program. Due to its size, it is impractical to save all
student input from the program. A save command is used at those inputs where the response would
be indicative of the student's progress or where necessary revision is anticipated. According to
the placement of the save command, a student's input is either stored unconditionally or only if
a correct response is not found- Fifty inputs use the save command in the program.

Development

The production of the first version of the program extended over several months. Its
development can be traced through various stages- The initial stage has already been mentioned,
that being the choice of topic. Following this, research was done in several mechanics texts to
reveal the varying methods and aspects of the solution. A general plan was formulated and then
sketched in flowchart form- Next, the major portions of the text were written on paper. This was
incorporated in the production j •

428

Preview: spring forces , mmtlE\

HARMONIC MOTION, UI'.GRl'EG OV

^ fri;edom

^introduction to the systems

V TO BE STUDIED J

[ DISCUSS ION OF COORD! NATf%
SYSTEM, SIGN CONVENTIONS^/

^WRITE THE EQU,

ftTIONS OF MOTION**

CERf

'ERMINOLOGY : COUPLED

INEAR PI FEE RENT I AL

, jiOMOGENOTsN
EQUATIONS J

** students asked how tc proceed
. E. HOW TO GET SOLUTIONS FOR POSI
OF BODIES AS FUNCTIONS OF

/t’IND ANOTHER COORDINATE SYSTEM^
V NOTION OF NORMAL COORDINATES J

''ADD AND SUBTRACT EQU'ATIONS OF MOTION
IDENTIFY NORMAL COORDI ANTES AND
^ NORMAL FREQUENCIES

"OBTAIN CONFIGURATIONS AND INTERPRET^
*them physically - DEFINE NORMAL MODES

j^JfOD AND SUBTRACT SOLUTIONS T?S^
f EQUATIONS OF MOTION IN NORMAL \
1 MODES TO OBTAIN SOLUTIONS FOR 1

V POSITION OF BODIES RELATIVE J

\^T0 EQUILIBRIUM POSLTIGNS

/''write assu:

(SUBSTITUTE I!

'■---D SOLUTIONS ANON
^ THE EQUATIONS OF )
MOTION ^

^HOW DO YOU SOLVE FOR THE FREQUENCY^

^ FORM AND EVALUATE N

^DETERMINANT OF COF.FFI C I ENT^/

f SOLVE FOR RATIO OF

Amplitudes in each equation.

(OTHER POSSIBILITIES

^GET CHARACTERISTIC FREQUENCIES^

^OBTAIN CONFIGURATIONS AND INTERPRET
THEM PHYSICALLY -_DE FINE NO FMAL MODES,

(JSdd and subtract solutions

EQUATIONS OF MOTION IN NORMAL
MODES TO OBTAIN SOLUTIONS rOR
POSITION OF BODIES RELATIVE
SiTO EQUILIBRIUM POSITIONS

FIGURE ONE

of a complete flowchart where all branches and text were diagramed. The full flowchart, twenty-
five pages of large paper, took about two weeks.

Discussion of the material with colleagues was used at all stages and on the basii of
comments on the full flowchart a revised flowchart was Bade. A lore explicit indication of the
directives was included. A secretary used this aaterial to type in the code for the progran
which was stored on disk. This is the standard procedure for the project and is described in
detail elsewhere [5] . It took the secretary about a week to enter the bulk of the aaterial, the
file containing around 2,100 lines. The author then began debugging and filling in portions of
the program. Because of its size, the file was broken into several snaller files, the advantages
being that the snaller files could be corrected and reasseabled individually and that with an
overlay structure the entire program need net occupy core at one tine* A new file was created
for linking the various files.

It took approxiaately one working aonth to obtain the first running version of COUPOSC.
This implies that all syntax and prograaaing errors had been eliainated but says nothing of
graaaatical or logical errors. The progran was executed repeatedly by the author, nenbers of the
project and visitors. This .uncovered aost obvious errors and onissions. The progran was
constantly corrected for these over the initial testing period of about two nonths.

At the end of this period the progran was still far froa finished. The usage up to this
point had not included a substantial nunber of students to whoa the aaterial was fresh, but
instead has involved faculty or students a 1 ready knowledgeable on the subject. Usage by virgin
students is the only way the progran can be evaluated and revised effectively, fievision based on
student responses reguires scrutiny of the feedback and is the only way that truly responsive
and viable dialogs can be developed.

Student Usage and Feedback-Based He visions

The first class exposure was in the spring 1971. The program was optional, one of several
alternative ways of learning the naterial. The response files indicated about forty users in
that tine period. The material stored by the save commands was voluminous.

Careful analysis of this data is necessary to uncover points in the progran where there are
pedagogical weaknesses, questions which are unclear to the student and points where nore
assistance is needed. It must be realized that the author's own way of thinking is very nuch
reflected in the aaterial he produces. Aside froa the difficulty of spotting one's own mistakes,,
the weaknesses or obscurity of a particular sequence in a dialog nay be invisible to the author.

The data available concerning student performance is of three types. Free fora student
conment provides the aost direct information on where the prograa has difficulties. This coanent
can cone either at the end of the progran, where connents and suggestions are solicited or in
questionnaires handed out in class, Coaaents are delivered in person also. Secondly, student
inputs (or lack of) are an indication of their performance. A third useful datun is provided by
counters. These are stored internally and allow us to see how aany times a student repeated a
question.

If response information indicates that a large nunber of students have difficulty with a
certain input, analysis nust be made to uncover how the progran is failing. Possible
explanations are; (1) a correct response is not being recognized, (2) the question is unclear to
the student and (3) there has been inadequate or insufficient preparation for the question.
Host revisions were based on the first type of difficulty. However, it was felt that the most
iaportant revisions dealt with the latter two categories. All categories will be discussed
individually with examples.

A aajority of the revisions done on the basis of student feedback were the recognition of
new foras of the correct response. The revision sonetiaes involved simply the addition of new
strings to be recognized. In places where the matching structure is inadequate to handle a
variety of responses, the sequence say have to be entirely rewritten, making it more complex and
versatile. For tree-response questions, examinations of student input for unanticipated
responses is essential since there will invariably be a myriad of ways of stating the answer
which cannot be anticipated. Likely or indicative foras of incorrect answers should be sought
and responded to.

An example in COUPOSC of an input where the addition of new words to be matched was
sufficient is a point where the student is asked how the masses move relative to each other in
the lower frequency normal node. Originally, only five words were recognized. During the initial
usage, many other possibilities were discovered and now there are over twice as aany possible
correct responses.

430

A aore involved revision caae at a crucial point in the prograa. The student was asked how
he would like to solve the set of coupled differential equations of notion. la the first
version, several words and conbinations of words were recognized as suggesting possible aethods
of solution. The coding took about fifty lines. On the basis of student data a aore complex and
coaprehensive seguence was devised. The coding related to this input now nuabers around 200
lines.

Questions of a general or open-ended nature tend to bewilder the student who is not
following the aaterial very successfully The student sees the question as nebulous and has no
idea of how to respond. Inputs at these points often show things like "help” or ”l"a lost". It
is difficult to anticipate such points and so analysis of student data is necessary to uncover
such spots.

tfe consider a particular input in CoOPOSC as an example. After disclosing the objective of
finding out how the systea aoves, the student is asked how to proceed. That is, what shall we do
to find out how the systea aoves. It was found that aany students did not know how to respond to
this question. Though students night realize that the equations of notion would be needed
sonewhere in the solution it was not clear to then that this was the starting point. Thus, it
was felt that a aore specific and suggestive wording of the question was needed. This would
allow aore students to guess the answer without having to be told. In the revised edition the
student was asked to coaplete the sentence, "In nechanics, we usually begin by writing...”
Subsequent use of the prograa indicated a substantial inprovenent in student response.

Inadequate preparation leading up to a question is also a cause of poor student response.
The nature of the aistakes in the input can be indicative of what the student is aissing, and
aaterial to clear up the uncertainty can then be included. Whether the aaterial is included as
a reaedial sequence, or whether it is preparatory aaterial which all students are exposed to
depends on the nature of the aaterial and the nuaber of students showing a need. We try to
strike a balance between exposing students to aaterial which they eight already know and
preventing soae students froa even atteapting a response because of inadequate preparation.

As an exaaple, it was found that when students were asked to enter the equations of notion,
uncertainties about the nuaber of forces acting on a single body and the dependence on relaxed
length of the spring were exposed. A brief section asking about these issues was thus included
just before the question. Hopefully, any confusion about the natter is now exposed and corrected
prior to writing the equations of notion.

Conclusion

Bhat I have attenpted to convey in this paper is that writing a dialog is a sizeable task
which requires careful consideration and conscientious revision in order to produce aaterials
which are pedagogically sound. It is felt that the dialog nethod of learning offers proaising
hope for education, but caution aust be exerted. Efforts in this direction nay represent no
inprovenent over the present situation or nay even represent poorer aethods of teaching if the
materials do not reflect the author* s diligence at Baking then responsive and tailored to the
student.

REFERENCES

1. Bork, Alfred H. , ”Conpu ter-Based nechanics," Proceedings of Conference on Coaputers in
Undergraduate Science Education. Published by Coaaission of College Physics, College Park,
Haryland, 1971.

2. Bork, Alfred H. , "The Computer in a Responsive learning Environaent — Let a Thousand Flowers
Blooa, ” Proceedings of conference on Coaputers in the Undergraduate Curricula, Dartaouth
College, Hanover, H.H.* June, 1971.

3. Honroe, Hark, "Physics Coaputer Development Pro ject-Coaputer Assistance in Student Problea
Assignaents, " Proceedings of Conference on Coaputers in the Undergraduate Curricula,
Dartaouth College, Hanover, N.H., June 1971.

4. Bork, A., and Sheraan, N . , "A Computer-Based Dialog for Deriving Energy Conservation for
notion in One Diaension," Aaerican Journal of Phvsj.cs.

5. Bork, A., Ballard, R., "PHYSICS COHPUTEB DEVELOPHENT PROJECT, " University of California,
Irvine.

4CiO

431

PROJECT CAPLIN: COMPUTER AIDED PHYSICS LABORATORY

INSTRUCTION FOR NON-SCIENCE MAJORS

V. E. Bron
Indiana University
Bloomington, Indiana 47401
Telephone: (812) 337-1304

Introduction

We have recently coapleted a set of coaputer aided laboratories for an introductory physics
course for non-science najors. Laboratories in the areas of kinematics, aechaoics and wave
notion have been developed and tested on large nuabers of students. Laboratories in the areas of
electricity, aagnetisi, theraodynaaics and selected advanced topics are to follow.

The laboratories contain what we believe to be unique features in conception and execution.
The following priaary tenets serve to describe the approach taken in the developaent of the
coaputer naterial. (1) Coaputer aaterial is used in conjunction with traditional laboratory
experiments used to illustrate physical concepts and laboratory practices. In this environaeat
the coaputer is aeant to enhance the student's laboratory experience: not to supplant it. (2)
The laboratory is a iced priaarily at non-science aajors (predoainantly pre-aedical students in
our case) . Consequently, the coaputer aaterial aust take into account the student's
disinclination toward (and often disinterest in) aatheaatical and physical aani pul at ions. (3)
The interaction of the student with the coaputer should closely reseable the student's aost
probable aode of interaction during his professional career. (4) The coaputer should not
undertake all computational and graphic tasks. Accordingly, alaost all of the coaputer prograas
of Project CAPLIN do require that students carry out either rough calculations, soae part of the
graphing, check hand calculated results with coaputer results or coabinations of these. It is ia
fact the interaction of such student participation plus accurate, fast, coaputer calculated
results which we find to be a tutorial behefit. (5) Aaterial developed should be readily usable
by others in the field. Accordingly, all aaterial has been developed using standard coaputer
languages and coanercial ly available coaputer coaponents.

In keeping with the fact that the students are not science aajors the various coaputer
tasks are all preprograaaed. Students are, however, able to asseable those parts of the prograa
they choose to use. In addition, to within the logical requirements of the prograa, the studeats
are able to skip randomly aaong various sections of the prograa, and if necessary, return to
earlier sections for revision, etc. Several error recognition routines have been incorporated
into the computer programming to insure that the student's interaction with the coaputer is as
free of frustrations as possible.

These features and others are discussed below.

Equipment

The coaputer equipment available within the laboratory consists of Model 33 ASR teletypes
coupled to external telephone lines via Model 1 1 3 A Dataphones. Each teletype is linked to a
Model 212 XY plotter aanufactured by the Tiae Share Peripherals Corporation [ 1 ) . Three teletype-
plotter units are available in each laboratory class to serve noraally a total of twelve experi-
mental teaas of two students each. Within the confines of the two-hour laboratory session each
teas is allotted approximately 10- IS ainutes of coaputer tiae. The equipment has been tested on
an average of 300 students per week. With ainor exceptions, the equipment has beea found to be
serviceable, rugged, though somewhat slow in inforaation transmission (110 baud;.

Currently the terminals, described above, have been linked to the tiae-sharing facilities
of the Coa-Share Corporation at Ann Arbor, Michigan. Programming of coaputer aaterial has been
carried out using XTRAN which is an extended FORTRAN language available on the Coa-Share ZDS 940
system. Recently, we nave also transcribed all aaterial into FORTRAN for operation on the CDC
6600 Intercom system of Indiana University's Research Coaputer Center. In so doing, we have had
to write or adopt various interaediate level prograas to simulate features noraally available
under XTRAN. In particular, these include syntax error detection, escape, plotting, and free
formating routines. For the last named we have adopted the prograas reported by Smith[2].
Conversion was readily carried out within a period of roughly one aonth.

Although the equipment has served well the initial requirements of the project, it
possesses two easily recognizable disadvantages: slow rate of inforaation transfer aad
consequent high cost of computation. The initial average cost on the coanercial tiae-share
system was approximately $2 per student per laboratory (not including terminal costs).

A major bottleneck is the 110 baud rate of the teletype terminal. On the other hand, we
find that students appreciate the availability of hard-copy teletype and plotter output for
future referral and for inclusion in the laboratory reports.

In order to economize it was necessary to shift some terminal instructions to mimeographed
hand-out sheets, and to curtail the scope of some calculations, plots, simulations, etc. Many ot
these features could be reinserted providing a faster, inexpensive terminal were available.
Toward this end we have briefly experimented with a Tektronix Model 4002 graphic display unit.
Although such CRT display terminals provide the possibility of more rapid information transfer,
they appear to be of little use in our environment unless hard-copy capabilities are included.

Programmed Laboratories

General Features. A total of 12 laboratories have been programmed to date. The individual
programs will be listed in some detail in the next section. First we discuss general features
common to all programs. These common features are incorporated into subroutines available upon
call from a common CAPLIN library. Among the major of such common features are the following:

A sign-in and sign-out procedure which serves to initiate and end the program for the
student, identifies the student and determines the elapsed time of each usage of the
program.

A syntax error detection routine is applied to each line of entry carried out by the
student. A message is given describing the nature of any error and a request for re-
entry of the last line. This feature is particularly important when long data lists
must be entered. Since many non-science majors are not adept at numerical
manipulations, line by line error detection helps to alleviate student frustration
during terminal interaction.

A data acquisition routine allows presetting of minimum, maximum, as well as fixed
number of required data entries. This routine is particularly useful for entry of
data in tabular form. The routine automatically requests entries until the preset
number of entries per line and number of lines is satisfied. If the total number of
data entries is to be fixed by the student, the routine counts the number of such
entries and returns that number to the main program.

All programs are subdiv
analysis, data reduction,

A routine called CHOICE
to decide whether or not t
use a particular part,
permits random access (aga
and/or following parts. A
tabular display of the red
out the latter on his own.

ided into parts. These par
tabular display, graphic di
permits the student (within
o use any particular part
he is required to call u
in within the logic of the
s an example, a particular
uced data, but to skip over

ts may include
splay, and sin
the logic of
If the student
p a new part,
total program)
student may ch
the plotting

data entry, error
ulation sections,
the total program)
decides not to
The latter feature
to any proceeding
oose to obtain the
routine and carry

5. During execution of any of the parts, the student may also switch to any of the other
parts of the program through the ESCAPE feature. This feature is accessed by
depressing the escape key, or typing ESC, on the teletype, which automatically
returns the program to the CHOICE subroutine described in the preceding paragraph.

6. A number of plotting packages have been developed with which the program author can,
with a very small number of calling statements, produce graphic display of the
experimental data and calculated results. One such plotting package called GENPLOT is
also available to the student for the plotting of an array of X-Y points either
directly or with a least-squares fit to the points.

Computer Aided Laboratories. The following is a list of the main features of each of the
computer aided physics laboratories programmed and tested to date. An error analysis of the data
is normally available in the following laboratories, even where it is not specifically mentioned
in the description.

1. Computer familiarization. A single ten minute session is required to familiarize the
student with the mechanics of the teletype and the plotter. The program also
introduces the student to error messages, the CHOICE routine, data entry in tabular
form, and plotting of graphs.

2. Measurements laboratory. Nominally this laboratory involves the measurement of the
dimensions and density of a number of objects and with a variety of instruments. In
actuality the laboratory is used to instruct the students in the concepts of data
error analysis. The meaning of average value, mean deviation, and percent error are

432

ERLC

434

illustrated, flost subsequent laboratories include error analysis routines which are
optionally available. The teaching of error analysis and data value and the
relatively rapid understanding of the subject by the students has been one of the
major tutorial benefits of this project.

Concurrent Forces, The laboratory uses a simple force table consisting of two or sore
weights hung by strings to a central ring. The strings pass over roller-bearing
nounted pulleys. The object of the laboratory is to find experimentally the resultant
of three forces in equilibrium, to obtain the force of friction of pulleys on the
force table, and to determine the direction and magnitude of an unknown force. The
computer is programed to calculate the resultant of three forces which the student
claias to have so placed on the force table as to be in equilibrium. The student
aust, however, first enter his value for the resultant force. The computer then
prints out its value as a comparison.

Next a computer aided exercise is performed to deteraine the aagnitude and direction
of an unknown force required to balance three known forces. In an optional exercise
the force of friction is determined. The student finds the slope of a graph of the
weight of the hanging aasses vs. the incremental weight required to bring the systea
out of equilibrium. The results are checked against those obtained by the computer
using a least square analysis of the data. A computer based plot is also available.

Uniform Acceleration. The laboratory involves the rather traditional experiment of
the measurement of the acceleration of gravity by studying the motion of a body along
an inclined linear air track(3]. Progress of the aoving body down the track is
recorded on a strip of spark sensitive tape. Before entering data into the coaputer,
students are urged to scan their data to ascertain that the second differences of the
position of the moving body as a function of time are roughly constant. The computer
program also carries out the above, and if a preset number of second differences
exceed a preset deviation from the average value, then the student's data is
rejected, and a teletype graphic display of the data points is given.

If the data points are acceptable the coaputer program can calculate incremental
velocities and acceleration, an error analysis of the acceleration, the acceleration
of gravity, and the percentage differences between the accepted value and the
experimentally obtained value of the latter. The results are available in tabular and
graphical form.

Newton's laws. Apparatus for this experiaent closely follows that of the experiment
on uniform acceleration. Spark tapes are nade of four runs during which the
accelerating force (a hanging weight) on the aoving body is increaen tally increased
while keeping the total mass of the accelerating body and hanging weight constant.
The experimental data leads to the deterainati on of the acceleration of the moving
body under various forces, the acceleration of gravity and a check of Newton's force
law. The computer scans the data froa each of the four sparker tapes for constant
second differences. If the data is acceptable the velocity of the body as a function
of tine is determined and displayed in either (or both) tabular or graphic form. A
graphic display of the acceleration as a function of the mass of the accelerating
force is also available. The latter leads directly to the determination of the
acceleration of gravity, which is left to the student to calculate fron either the
tabular or graphical displays.

Momentum Ballistics. Studies the law of conservation of momentun and the elements of
projectile motion. Specifically the initial velocity of a projectile is determined
by two methods: (1) through a measurement of its range and vertical distance of
flight and (2) through a measurement of the displacement of a ballistic pendulum. In
the experiment a spring-gun ballistic pendulum is used as apparatus [ 4] .

The computer is programmed to carry out an error analysis of the experimentally
obtained range of the projectile notion, and of the maximum height of the ballistic
pendulum. The system then calculates the initial velocity of the projectile based on
the two methods and the percent difference.

A further check on the equations of notion is accomplished as follows. The initial
velocity of the projectile is varied by changing the tension of the spring in the
spring-guns among the apparatuses throughout the laboratory. The projectile range as
a function of the initial velocity, as obtained by the various experimental teams, is
then plotted on the computer system by the laboratory instructor.

A variation in the experiment is possible by using the computer to calculate the
expected range of the projectile, based on the results of the pendulum. The student
then returns to the apparatus to check the validity of the prediction.

433

435

Uniform Circular notion. Laboratory to determine the centripetal force and
acceleration of a body undergoing unifon circular lotion. A centripetal force
apparatus mounted on a variable speed rotator is used[4). In this apparatus a spring
(attached to the rotating body) provides the centripetal force. The latter is
calculated by the computer fro* the experimentally determined rotational frequency,
mass of the body, and radius of circular notion. The computed value is checked
against the value calculated by hand by the student. A similar determination is made
for the static gravitational force required to cause the same extension of the spring
as in the dynamic part of the experiment. A computer based optional simulation
experiment is available. The experiment involves graphed results of circular orbital
motion of a satellite or planet. The student is free to fix the orbital velocity of
the body, and the gravitational mass.

Torsional Pendulum. A laboratory to determine the period of torsional vibration, the
factors which determine the period of vibration, the torsion constant of a thin rod,
and the rotational inertia of various objects [4]. The computer is programmed to
calculate the rotational inertia of discs, cylinders, rings and various combinations,
rotating about a rod passing through their axes and also about displaced axes. In
addition it determines the period of vibration and the torsion constant of the
support rod. Optionally available is a calculation of the torsional modulus of the
material of the rod.

Two-Dimensional Collisions; Scattering. Experimental apparatus consists of a hidden
cylindro-polygonal object at which the student projects small steel balls [5]. The
scattered projectile leaves marks on pressure sensitive paper which rings the unknown
object. Students determine the angular location of the maxima in the scattering
distributions. From these it is possible to determine the shape of the polygon and
its orientation with respect to the trajectory of the projectile. The computer is
programmed to check the students* determinations. However, the student is forced to
determine the number of sides of the polygon before the computer becomes available to
him. An error analysis is optionally available, as is a determination of the
dimensions of the object providing the angular location of the "shadow" is supplied.
The "shadow" is the location of the scattered distribution of projectiles which just
miss the unknown objects on two sides.

Simple Harmonic Motion. Apparatus consists of two springs and various weights. The
aim of this experiment is to obtain the spring constants of each spring and that of
the springs combined in series. Two methods are used; (1) measurement of the period
of harmonic motion for various weights, and (2) static displacement of the spring for
various weights. The computer system is optionally available for plotting of data,
and for least square determination of the spring constants using data from the two
methods.

Wave Motion. Aim of the experiment is to check the equation of wave motion for
standing waves of a vibrating spring. Apparatus consists of a string held in tension
by a weight and forced to vibrate by one side of an electrically driven tuning
fork[4]. The string is "essentially" fixed at one end by the tuning fork and at the
other end by a pulley. The student measures the density of the string and the weight
required to bring the string to vibrate in its fundamental mode, and various
narmonics. The computer is programmed to calculate the tension in the string, the
velocity of propagation of the displacement, the wavelength, and frequency of
vibration. A check is available on the experimental masses through a calculation of
the mass required to obtain the above results. A plot of velocity vs. wavelength is
also available tor a graphical determination of the vibrational frequency.

Velocity of Sound. Laboratory to determine the velocity of sound in air, and to study
standing waves in a tube open at one end[6] . The apparatus consists of a glass tube
in which a column of water can be adjusted to any desired height. The student
measures the length of unfilled tube required to fulfill the fundamental, and several
harmonic, resonant conditions. This is done for a number of different sound
frequencies (tuning forks) . From the measurement the velocity of sound can be
abstracted. The computer is programmed to carry out the calculation of the velocity
of sound corrected for the temperature of the room. A computer simulated experiment
is also available. In the latter, the computer plots out a graph of two sine waves
differing in frequency by a small amount. It also plots the sum of the two sound
waves, and its envelope to illustrate the beat frequency. The student is then
required to return to the laboratory, obtain a second sound column, an.d check for the
occurence of the beat phenomenon.

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436

Conclusion

A survey of student reactions to Project CAPLIN has been carried out by direct observation
in the laboratories, by discussions, and by a foraal questionnaire of 300 students involved. He
do not claim, however, to have carried out a thoroughly conceived and tested statistical survey.
Nevertheless *a have gained sole insight into the benefits of the project to the students and
their reactions to it.

Perhaps tha aost easily recognizable benefit is the rapid rate at which the students
learned to understand and appreciate the error analysis of experimental data. This result was
achieved through consistent application of data error analysis as taught to the students during
the measurements laboratory discussed in the previous section. Hany students eagerly awaited the
print out ot the percent error in the data, and quite a nunber actually repeated experiments (in
a knowledgable manner) when significant error was indicated. Such results had not been possible
prior to the implementation of the computer system. In the past, data error analysis was
normally neglected in order to maintain a reasonable duration for any one laboratory. Even when
such error analysis was included as a long hand exercise it vas seldom possible for the student
to rerun the experiment within the time limitation.

A second readily appreciated benefit of the project has been the tutorial aspect of
computer based graphing. By providing the student with accurately plotted graphs at various
phases of the program, and by requiring abstractions from or additions to the graph, it has been
possible to help the student to become familiar with graphical representation of physical
concepts. We have observed that many non-science majors have had only limited previous exposure
to such knowledge. We are currently further refining the techniques used in student-graphics
interactions.

Students also found it advantageous to their understanding of the experiment to have
available accurately calculated results of some phases of the total data reduction. In almost
all laboratories, student participation is required through additional calculations. The
availability of some calculated results serves as a useful guide against which to measure their
understanding and the accuracy of the results of the additional calculations.

Finally, the increased rate of comprehension in the areas discussed above, plus the
inherent saving of time in calculations performed by computers, allowed us to expand a nunber of
the laboratories. The expansion has taken the form of either increasing the duration or
complexity of the experimental phase of the laboratory, or in carrying out simulated allied
experimentation on the computer system. In this way, it has been possible not only to enrich the
laboratory experience of the student, but also to cover additional physical principles and their
extension s.

REFERENCES

1. Time Share Per ipher ials, Wilton, Connecticut.

2. Computer-Based Physics; An Anthology# Ed. R. Blum, Commission on College Physics, September
19697

3. Manufactured by The Ealing Corporation, Cambridge, Hassach uset ts.

4. Manufactured by Central Scientific Company, Chicago, Illinois.

5. Manufactured by Welch Scientific Company, Skokie, Illinois

6. The experiment follows the discussion in Chapter 20 of "Physics* Part 1, by R. flesnik and
D. Halliday, John Wiley and Sons, New fork, 1966, page 509 ff.

437

435

A CDHPUTEB ASSISTED IBSTBUCTIOB PBOGBAH IB
AHEBICAN HISTORY, 1870-1921

Betty L. Jehn
University of Dayton
Dayton, Ohio 45459
Telephone; (513) 434-4520

This instruction prograa is an attenpt to demonstrate the adaptability and versatility of
the computer in a field other than science, and by so doing to provide a new approach to the
learning of Aaerican History. This prograa is designed as a study aid and hopefully it will
enable the student to find deeper meaning and understanding from a textbook and classroom
instruction.

In the past five years there has been a shift in the philosophy of education in the United
States, but it seems that the technology of education has not kept pace, at least on the college
level.

With the increasing awareness of disadvantaged groups in our society, our approach to
education has shifted from establishing simply mass education to providing quality mass
education [ 1 ] «> one result of this new approach has been a change of administrative attitude on
the college level from high-selectivity for admission to more opportunities for the less veil-
prepared students. Consequently, numerous problems have arisen among which are increasing
enrollments and rising costs.

These increased costs; the need to educate more people from different backgrounds and of
different ages; the fact that the body of knowledge in all disciplines is expanding even faster
than the body of students; the fact that the teacher of tomorrow must present more information
using the same period of tine that he uses today; and the limited resources of equipment and
personnel, all these demand some new approach to the solution of the problems of education*
Educational technology and computers in particular hold forth a promise of that solution to the
humanities as well as to the sciences.

As other types of education technology have proven less than ph( uonenally nvccessfjul,
educators have turned more and more to the computer. The computer has capabilities undreamed of
even by the computer specialists of just a decade ago.

The history profession in recent years has been modernizing to the extent that ethnic
studies, area studies and comparative studies are being incorporated into the courses. But the
great problem in teaching is coaaunica ting with and motivating contemporary students.

Two young professors at Orange Coast College, Costa Nesa, California express the problem in
this way:

At a time when people spend a greater portion of thr»ir lives before television tubes
than in educational institutions, instructors lull students to sleep with lectures
such as were designed for information transferral prior to the invention of the
printing press. Bhile the public is accustomed to sophisticated motivational
psychology from Hadison Avenue, instructors rely upon prinitivo reward-punishment
mechanisms to interest students in learning. And while the public is effectively
tied to instantaneous electronic data systems, students are asked to crowd their
minds with raw data as if it contained some inherent meaning.

SQch poor allocation of resources is grossly inefficient and really indefensible.
Historians like others operating in the twentieth century, ought to exploit the
knowledge, skills, and tools available to them for relating their discipline to their
students [2] .

Dr. Robert D. Hess, professor of psychology in Stanford University's school of education
and a colleague. Dr. flaria D- Tenezakis have found that a group of junior high school students
aged thirteen to fifteen associated the computer with such human qualities as trustworthiness,
reliability, veracity, and fairness. The study further indicated that the youths rate the
computer as a "more positive source of information" than their teachers, textbooks, or
television news reports.

The use of technology in education and particularly that of the computer for
instruction, vill continue to expand. Thus the adaptations that the child develops
in his responses to machines become of special interest.

439

436

These are crucial aspects of the socialization of the child into nodes of dealing
with an industrial aighly technological society. The points of contact between the
child and the institutions of society will be increasingly eechanical. Thus the
aachine takes on tha role of an authority figure [3] .

As a result of these observat ion s, the decision was aade at the University of Dayton, in
the spring of 1970, to atteapt a Computer Assisted Instruction prograa in American history as a
master's thesis. As of that tiae, as far as *e were able to ascertain, little or nothing had
been done in the field of history in CAI. By rationale for choosing two seeaingly far reaoved
disciplines in which to work was aanyfold: I was working in Aaerican history; I needed
something new and different to use as a thesis; I had an interest in coaputers and coaputer
science; and the University of Dayton has an RCA Spectra 70/46 coaputer which has the capability
of accoaaodat ing CAI. Everything seeaed to point in one direction and the chairaan of the
history department was receptive to the idea so I vent ahead.

When we began this CAI experiaent in Aaerican history, it was decided to prograa it in
DAS 1^ • BASIC was chosen for two reasons: the prograaaers were faailiar with it and it is
compatible with the RCA Spactra 70/46. Two coaputer science students, Karen Sudzinski and
Frances Gundy, did the prograaaing for this course. It was used as their special project for a
course in Advanced Prograaaing.

As a basis for the questions in this prograa the History Su§t§£X Set i
written by Dr. Wilfred J. Steiner of the University of Dayton were used. The textbook by
Samuel florison and Henry Steele Coaaager, <i£ow£h $1 £he Aa££ic*fl Republic, Vo^ U- New York,
1969, was also used in order to verify thu arrangement of the material. Any other text could be
used and the aaterial rearranged to fit. A fact is a fact and will be found in any reliable
textbook.

This program in Aaerican History begins at the end of Reconstruction and ends at the Treaty
of Versailles. It consists of eighteen separate parts or lessons. As each part requires a
great deal of coaputer storage space, only the first seven were put on the system in the
beginning. The remainder are 3tored on decks of IBB cards and can be put on the system at a
moment's notice. Because of this physical storage problem, it is recommended that only a
certain number be put on the system at a given time. For example, five lessons could be put on
at the beginning of a term; at the end of a period of time when the instructor felt that the
aaterial had been covered in class; lesson one or perhaps one and two could be taken off and six
or six and seven added. This is accoaplished very quickly and easily. It is always possible to
put the programs back on the system and perhaps a day or so before an exam, the entire group of
lessons could be put on for further study.

By dividing the History Prograa into various segeaents, it becomes easier to handle than
one continuous prograa. This is especially true if it is to be used on a systea smaller than
the RCA Spectra 70/46. A’io by having small lessons, revisions and alterations can be very
easily accoaplished. Because the instructor himself can revise and alter the prograa, it
becomes not a standardized, stereotyped instruction, but rather a course of study personalized
by the individual instructor.

The goal ot tutorial CAI is to individualize instruction and while interaction with a
coaputer is aore personal than for example, aerely watching a film strip, nevertheless the
personal quality is aissing. CAI will never replace a classroom teacher, but assuming that the
student will have access to aost of the information that can be offered in a specific course
froa a variety of sources, one can readily understand that this availability of educational
resources aust bLing about a change in the role of the instructor. The coaputer will relieve
the teacher of aany routina burdens thus giving hia additional tine and then the role of the
teacaer can change froa one who aerely imparts information to one who relates to the students,
and by so doing becoaes one who iaparts knowledge by managing the learning experiences.

In the case of a CAI prograa in his ory, the coaputer can impart the facts and events of a
certain period. But a group of facts is not history, however a student aust have a background
of events before these saae events can be interpreted. A teacher, therefore can be relieved of
the burden of fact presentation and can take the valuable classrooa tine for discussion,
theories, and interpretations * a aore in-depth coverage of the aaterial would thus be possible
in the saae tiae allotaent.

A prograa such as this can be of alaost unlimited value. When the situation arises wherein
there is a potentially good student but with a poor background in a class, the prograa could be
used to give such a student a quick grasp of fundamental faces. It could serve as a review of
fundaaentals which an average 3tudent should know, but does not. It could serve as a fast
review before a test. It could reinforce the learning process for a slow learner. With a few
alterations, it could be used is a placeaent test for a transfer student or a student with a
superior high school background. Further, university classes in the survey courses are

frequently large, this CAI program could supply the individual attention which would otherwise
be impossible.

This particular CAI prograa in American History consists of a series of questions and
answers. The student sits at a terminal and identifies himself to the computer by giving his
student number. He is then ashed which lesson he would lite to do. After typing in tha code
name of a lesson on the terminal he is ready to begin. The computer will ash a question which
will require the student to answer in one of several ways. Sometimes the question will be a
simple true or false; sometimes it will be a multiple choice; and soaetimes the student will be
required to supply the answer himself. The computer will then tell the student if he is right
or wrong, and if the answer is wrong tha student will be given the correct answer and in many
cases an explanation will be given.

A group of student** from a University of Dayton history course were ashed to use this
program during t e spring cere of 1970. About half of the students in one particular course
volunteered to use the CAI prograa. At the end of the tere, these students were ashed to fill
in a question! ire regarding the prograa. The results of the questionnaire were eost
encouraging. L n every case the students using the CAI prograa considered it "fun.H The
following are soie typical coeients eade by the students:

I really liked working the CAI progrue — it would be a good use for review.

I thought the prograa was was helpful, and helped reveal one*s weak and strong areas
on his knowledge of the segeent of history being covered.

X ferl that an attempt was made to set up a history prograa that was stimulating,
interesting and in general a fine attempt to bring technology to the student. As a
participant I thank you for the opportunity to learn just a minute portion of a thing
I have long held mysterious (The Computer)

X think that a history course using this type of program would be ;*ost worthwhile on
the high school leval. I don*t think that facts should be so emphasized in the class
work or exams of a college history course. X feal that analysis is more important on
the college level. A good background of facts should be gained in high school, and I
think high school students would find it to be a great help.

I think it could be a very good review for tests.

Just a lot of fun for a change! I really liked it and it proved how little I know in
history.

If this type prograa were to be used for future classes as study material, I think it
would be wise to have the students prepare some of the questions. The only criticism
I have is that if your answer is incorrectly spelled, but the name is correct, it is
not correct. But I would consider this a very minor criticism in comparison to the
help I consider CAI does.

The students using this program seemed to be very concerned when the computer told them
they were wrouq. They were expecially concerned if a question was counted incorrect if it was
merely misspelled. When CAI is explained to students in the future it will be wise to explain
that the computer accepts exactly what one tells it and not what one thinks he has told it.
Also that the program is for study and not a test and that they should not be overly concerned
if a misspelled word is not accepted. Some ordinary misspellings were included in the program
as acceptable, but it is impossible to anticipate all the variety of w?Ays a word can be spelled!
For this reason then, if this history program were to be used as a test, it is recommended that
questions be of true and false or multiple choice only to avoid the previously mentioned
possibilities or rejection for misspelling.

Ha have all accepted the premise that knowledge is ever increasing and at a fantastic
speed, therefore cur ways of imparting knowledge must necessarily change. An effective learning
experience i.j one in which a student will receive multiple exposure to the material. There is
nothing in a CAI program which could not be found in a textbook, but it is presented in such a
completely different way that it makes a different impression on a student, When the material
necessary fo*: the achievement of a learning objective is presented through a variety of media,
the probability that the student will get the multiple exposure necessary is greatly increased.
And because of the interaction of the student with the computer, it is a way of getting
something more than passive acceptance from a student.

Because the University of Dayton was among the first universities in the nation to have a
computer facility, I feel that it should also be in the forefront of computer usage. Since
computers are such a tremendous investment, they should be used in every conceivable way to make
the investment profitable.

OLO

OLO PROGRAM NAME--L ABOR01
REAOT

•RUN

WHAT'S TOUR Nt CKNAME7BET TY
WHAT IS TOUR STUOENI NUMBER 7
7 12345

ANSWER • TRUE* OR • FALSE* TO ALL TRUE OR FALSE OUESTIONS
UNLESS GIVEN OTHER' DIRECTIONS* ALSO GIVE ONLY THE LAST
NAME WHEN A FILL-IN REQUIRES A PERSON'S NAME*

1 * IN 1900 OVER ONE AND A HALF MILLION CHlLOREN UNOER 16

MERE EMPLOTEO IN FACT JRT OR FIELO IN THE U*S*

7 TRUE

I * M PROUO OF YOU* BETTY

2 . CHILO LABOR LAMS AROUNO 1911 APPljEO ONLY TO CHlLOREN

UNOER YEARS OF AGE* O/SE NUMBERS)

712

60-0

3 • I NOUS TF . AL ACCOENT'i MERE COMMONPLACE*

NO* NO- NO • BETTY

4 * THE KNIGHTS OF ST* CRISPIN MAS A UN \ ON OF «

7RAIL80A0 OORKERS

WRONG

IT*MAS A -JUI" N OF SHOEMAKERS ORGANlZEO IN 1867*

IT USEO REACTIONARY MEASURES ANO MAS NOT SUCCESSFUL*

5 • THE FOUR LARGEST .1AILR0A0 UNIONS WHICH ARE STILL

OPERATING T 00* Y ARE KNOMN AS THE A) RAILROAO BRO-HERHOOOS
4) RAILWAY LABOR UNIONS

7 A

RIGHT

6 • SAMU-L CONFERS ANO AOOLPH STRASSER ORGAN! cEO WHAT

GROUP- 1 N 1886 AT C-LUM3US * OHIO 7 (USE INITIALS
ANO NO-PER I 0« )7AFL
THAT '.S RIGHT

7 • MHO WAS THE FIRST ANO ONE OF THE MOST IMPORTANT

PRESIDENTS OF THE AFL 7G0MPERS

HE MAS PRES I OE NT FROM 1086 UNTIL 1924*

6 t MHO TOO- OVER THE PRESIDENCY OF THE AFL IN 1924
. AFTER GOMPERS 7S0RRY

THAT WAS A LITTLE ROUGH* HE MAS MILLIAM GREEN*

9 • TERENCE V* POM-ERLY MAS GRANO MASTER MORKMAN OF THE
OR-ANIZAT ION C-LLEO T HE l ‘

7CI0

THE ORGANIZATION MAS CALLEO THE KNIGHTS OF LABOR*

II • THE MAGE PRINCIPLE ESPOUSEO BY OAVIO RICAROO* THAT ALL
MAGES-TENO TO FALL TO THE LEVEL MHICH THE MOST UNSKILLEO
OR THE NOS- OESPERATE MAN WOULD ACCEPT ISi
*0 S-PPLY ANO OEMANO LAM
8) IRON LAM 0- MAGES
C« NEGATIVE MAGE P-INCIPLE
79

GLAD TO 'EE YOU GOT THE LAST ONE RIGHT I
YOUN SC"'E IS 60 l
YOU JON'T KNOM THIS TOPIC 7.0E0UAT -LY •

•BYE

ZBKPT P:OUNT 006572
/LOGOFF

IC E 42 0 LOGOFF AT 1508 ON 02/26/72* FOR TSN 3777.

IC E421 CPU TIME (SEC*) 2026*4133 CONNECT TIME (MIN*) 023
ZC E427 JUS.' SPENT S 1 *92 SPENT TO OATE 1220. 61-

FIGURE 1. Sample run of one lesson in the program: Labor*

439

UU2

010 PROGRAM NA ME ** I MM I G
RlAOT

•RUN

Nil MV NICKNAME IS SPECTRA* MHAPS Y 0URS76ET T T
MHAT IS TOUR STUOENT NUM9ER711345

PERSISTANT POVERTY FOR THE PEASANTS! RECURRENT HARO* T I RES
FOR MORKERS • MAR ANO THREAT OF Mill TART SERVICE ! POLITICAL
OPPRESSION* RELIGIOUS PERSECUTION ANO CLASS-SYSTEM MHICH CLOS*D
OOORS TO OPPORTUNITT MERE MAJOR MOTIVATIONS FOR EMIGRATION
TO AMERICA*

1 * NAME TMO OTHER COUNTRIES BESIOES THE UNITEO STATES
VHfCH RECEIVEO MANT IMMIGRANTS OURI*G THE NINETEENTH
CENTURT. (ENTER ONE COUNTRY PER LINE.)

7MEXIC0

7CANA0A

CANADA IS CORRECT BUT MEXICO IS MRONG*

OTHER COUNTRIES RECEIVING MANY IMMIGRANTS MERE!

AUSTRALIA
SOUIH AFRICA
ARGENTINA
BRAZIL

Z • C*EAP IMMIGRANT LABOR THREATENED THE GAINS OF ORGAN I ZEO
LABOR MHICH CAUSED UNIONS TO AGITATE FOR 7 OF
IMMIGRATION*

70U0TAS

CORRECT*

3 • IN THE OECAOE FROM 18S9 TO 1G6« TMO AND A HALF MILLION

IMMIGRANTS CAME TO AMERICA* (ANSMER TRUE OR FALSE*)

7TRUE

TOUR ANSMER IS RIGHT* ANOTHER 14 MILLION ENTERED
FRO* I860 TO 1901*

4 • IN THE GENERATION IMMEDIATELY AFTER THE CIVIL MAR! A

LA*OE NUMBER OF IMMIGRANTS TO AMERICA C*ME FRONi
A* NORTHERN AND MESTERN EUROPE
0* SOUTHERN EUROPE
7A

VERT 60*0*

5 • THE IRISH IMMIGRANTS TENDED TOl

A* BECOME FARMERS
B* SETTLE JN THE CITIES

7 A

MRONG* THE IRISH MADE LOUSt FARMERS*

6 • RAILROADS ANO STEAMSHIP COMPANIES ENCOURAGED I MMI GRAY 90*

BY THEIR ADVERTISING IN EUROPE* (TRUE OR FALSE)

7FALSE

HOM DO YOU THINK ALL THOSE POLLOCKS GOT OVER HERE 7
SAYt THAT REMINOS ME OF A GOOD POLLOCK JDkEi MHAT'S
A POLLOCK'S* I OEA OF MAICHEO LU0GAGE7****.**TM0 A£P
SHOPPING BAGS 1 1 1 1

FIGURE 2. Sample run of one lesson in the program: Immigration.

i *! * ’

443

440

? * LARGE NUMBERS Of GERMAN IMMIGRANTS CONGREGATED
IN THE ? TO BECOME FARMERS*

? M | DOLE WEST

CORRECT*

8 • LILLIAN D* MAID AND JANE ADDAMS M«RE EARLY CHAMPIONS OF t

A* SOCIAL REFORMS
8* POLITICAL REFORMS

YOU HAD A 5B-5I CHANCE OF GETTING THIS RIGHT AND
YOU BLEU I T I

9 • DURING THE LATE NINETEENTH CENTURY AND EARLY TWENTIETH

CENTURY* AS HIGH AS 7SX OF MINE LABORERS MERE
FOREIGN BORN. (TRUE OR FALSE)

7TRUE

ITA$ A GOOD THING YOU GOT THIS ONE RIGHT*

18 . THE IMMIGRATION ACT OF 1382 PROVIDED FOR A LIMITED

NUMBER OF IMMIGRANTS FROM SOUTHERN EUROPE (T OR F)

WRONG* THIS ACT PROHIBITED THE IMMIGRATION OF CRIMINALS
AND OTHERS LIKELY TO BECOME A PUBLIC CHARGE*

11 « *N ACT MHICH PROHIBITED THE ENTRY OF CHINESE LABORERS

INTO THE U*S* FOR A PERIOD DF TEN YEARS MAS ACT*

71 DONT KNOM

BETTY* YOU SHOULD HAVE KNOMN THIS ONE!

THE ACT MAS THE CHINESE EXCLUSION ACT*

12 * IMMIGRANTS FROM MHICH COUNTRY OF MESTERN HEMISPHERE
CAUSED THE M«ST PROBLEMS TO THE U*S* (MEXICO OR CANADA)

VMtXICU

NEX 1C* IS CORRECT*

13 • THE DIFFERENCES BETMEEN THE "OLD" IMMIGRANTS AND
THE "NEM" IMMIGRANTS«MAS STRIKING* DID THE DIFFERENCES
DISAPPEAR MITH THE SECOND 6ENER AT ION? (YES OR NO)

7ND

MRONG* THEY DID DISAPPEAR MITH THE SECOND GENERATION*

THE NUMBER MRONG * 7
YOUR SCORE IS 46 X*

ARE YOU GOING TO LET A COMPUTER DUT-SMART YOU?

TRY STUDYING THIS SHEET.

FIGURE 2. Continued

444

The President's Science Advisory Committee Report on "Computers in Higher Education" nates
abundantly clear the necessity of quickly introducing conputer instruction and time-sharing
conputer experience into universities, colleges, and high schools. The Report says,
"Undergraduate college education without adequate conputing is deficient education, just as
undergraduate education without adequate libraries would be deficient education."

A personal hands-on acquaintance with a conputer terninal should be part of the experience
of every college student.

FOOTNOTES

1. Lawrence P. Grayson, "A Paradox: The Promises and Pitfalls of CAI," Educon, V, No. 2 (March
1970), 0.

2. Michael G. Crow and Edward A. Burke, Jr., "Modern Methods can Make History Relevant,
Interesting," £4u£i£ional Hedia, VIII (Feb. 1970) 0.

3. Harvey Elnan, "These Students Trust Conputers, Call Then Reliable," Cgmputekwgcld , (Hay 6,
1970) , 25.

REFERENCES

BOOKS

1. Basjic Language, Iime-£ha£ing Service Bef erence Manual, General Electric Infor nation Service
Oepartnent, June 1965.

2. Bushnell, Don D. and Dwight if • Allen, The £ogj>uter ig American Education. New lork, 1967.

3. Caffrey, John and Nosnann, Charles J. Computers og Campus: A Report to the ££§sident on

Ik§.AE and Managenent. Anerican Council on Education, Washington, D. C. 1967.

4. Fink, Donald, Conputejrs and the Hunan Mind : Ag Introduction to Art i fiscal Intelligence,

New York, 1966.

5. Lekan, Helen A., ed. Index to Conputer Assisted Instruction. Instructional Media

Laboratory, The University of Wisconsin-Nil waukee. Second Edition, Sterling Institute,
Feb., 1970.

6. Horison, Sanuel and Henry Steele Commager, Growth of the Amey jean jc. 2 Vols. , New

York, 1969.

ARTICLES IN periodicals

1. Anderson, G. Ernest, "Conpu ter-Assisted Instruction: State of the Arts." flat jon's Sc^gols,
LXXXII, (October, 1968), 50-54.

2. Blaschke, Charles, "conputers in Education: Interesting, But How Relevant?" Educational
Technology, IX (May 1969), 5-0.

3. Carson, Linda, "CAI — What It Can Do for Education" Educational Media, I, (October 1969), 6-

4. Crow, Michael G. and Edward A. Burke, "Modern Methods Make History Relevant, Interesting"
educational fledia, I, (Pebruary 1970), 0-10.

5. Elman, Harvey, "These Students Trust Computers, Call Them Reliable,." Computer woy Id (Hay 6,
197 0), 2 5.

6. Peingold, Samuel L. , "Planit — A Language for CAI," Datamation, XIV (September I960), 150-
154.

7. Fryo, Charles H., "CAI Languages: Capabilities and Applications," Datamation, XIV

(September I960), 140-145.

8. Gilman, David Alan and Nancy Ann Morean, "Effects of Reducing Verbal Content in Computer-
Assisted Instruction." A V Communication Review, XVII, (Pall 1969), 16-20.

ERIC

445

442

9. Grayson, Lawrence P., "A Paradox: The Promises and Pitfalls of CAI," fdggs*. V (March

1970) , 1-3

10. Herman, Don, "Cincinnati Students Vie For Computer Tine," B&dAA* I (September

1969) , 4-7.

11. Inman, Richard P. , "Conpu ter-Assisted Education at the Naval Academy," fctago&» IV, (March
1969) , 1-4.

12. Kanner, Joseph H., "CAI — The New Demonology?" figtgngtion, XIV (September 1966), 151-154.

13. Kantor, Seth, "Blueprint for Revo ul tion , " Sducatiggai 3§4i5* XI (April 1970), 3-b.

14. Luskin, Bernard J. , "Coaputer's Educational Role Confused by the Lack of Standard

Definitions." Conpu te^wor id, January 15, 1969.

15. Luskin, Bernard J., "Tne Tine is Now for Developaent of Computer Assisted Learning,**

Coffl£Uterwo£ld, Noveaber 17, 1968.

16. Menkhaus, Edwin J., "The Computer Kids: Most Likely to Succeed" Cgn£ijte£ Biagst, (October

1968) , 1-2.

17. Morrison, H. tf. and E. M. Adaas, "Pilot Study of a CAI Laboratory in German," Jhe Hodgpn

Language Journal, LII, (May 1968), 10-12.

18. Oettinger, Anthony and Sena Marks, "Educational Technology: New Myths and Old Realities,"
Harvard Educational Review , XXXVIII (Fall 1968).

19. Riedesal, C. Alan and Marilyn n. Suydam, "Coapu ter-Assisted Instruction: Implications tor

Teacher Education," The AtiliLBSlAS l£3£il££# (January 1967), 1- 10.

20. Rogers, James L. , "Current Problems in CAI," Datamation, XIV (September 1968), 130-133.

21. Smith, J. Stanford, "The Growing Maturity of the Computer Age," Cgmputeg gigest (November
1968) ,3.

22. Suppes, Patrick and Mona Morningstar, "Computer- Assisted Instruction," Science, CLXVI, No.
3903 (October 17, 1969), 348.

23. Vannan, Donald A., "Educational Media in the U.S." Educational fledia, n (April 1970), /~B.

24. Zinn, Karl L. , "Instructional Uses of Interactive Computer Systems," Datamation. XIV,
(September 1968), 145-150.

UNPUBLISHED REPORTS
U. S. GOVERNMENT DOCUMENTS

1. Alcorn, Bruce K. , "The Small College and the Coaputer — An NSP Experiment," Report on a

National Science Foundation Grant. SRE3, 1969.

2. Becker, James W. , "Run Computer Run: A Critique," Presentation for the Conference on

Information Technology and Secondary Education, May 1-2, 1968. Sponsored by Harvard

University's Program on Technology and Society.

3. "Coapu ter-Assisted Instruction at the Plorida State University* IBM, Application Brief.

4. "Computer- Assisted Instruction, N octh/South/East/West, " The Proceedings of Four Regional

Conferences of ENTELEK CAI/CMI Information Exchange. 1969. Entelek Incorporated

Newburyport , Mass.

5. Entelek, CAI. CHI Newsletter" November 1969

6. Hickey, Albert E. , et ml., "Computer-Assisted Instruction, A survey of the Literature,

Entelek, Incorporated, Newburyport, Mass., Defense Documentation Center. Defense Supply

Agency.

7. Kopstein, Felix F. , et al., Computer-Administered Instruction Versus Traditionally
Administered Instruction: Economics, Georgia Washington University, Alexandria, June 1967.
Defense Documentation Center. Defense Supply Agency.

^4^

446

tt. flajer, Kenneth and Duncan Hansen, "A Study of Conpu ter- Assisted, Hulti-nedia Instruct ion"
augmented by paper presented at the American Education Besearch Association Annual
fleeting, Los Angeles, California, Pebruary 1969*

9. flarcus, Robert L., "Summary Report," Entelek CAI/CHI Infornation Exchange, Midwest Rngional
Conference, 1969-70.

10. Nevinson, John H. , "Demonstration and Exper inentation in Conputer Training and Use in
Secondary Schools." Secondary School Project Interin Beport (No. 3). October 1, 1968.

11. Plyter, Nornan, "CAI Program of the State University College at Brockport, N.Y." Sunnary
Deport, October 3, 1969.

12. Bichardson, Jesse 0., "aodern Trends in Education, One-Year Schoolvide Project, Grades K-
12, Conputers in the Classroom." Science Besearch Associates, Inc., flarch 15, 1968.

13. Bichardson, Jesse 0., "Progranned Instruction and Learning Systens, One Year Schoolwide
Project," Science Research Associates, Inc., Chicago, April 15, 1968.

14. Bosenberg, a. C. , et al, "Investigations in Computer-Aided Instruction and Conputer- Aided
Controls*" USAF Bedford, flassachusetts, April 1967. Defense Docunentation Center, Defense
Supply Agency.

15. Seidel, Bobert J., "Coaputers in Education: The Copernican Bevolution in Education

Systei." Professional Paper 16-69, flay 1969.

16. Silverman, Harry P. , "Applications of Conputers in Education." Systens Developnent
Corporation, Santa flonica, California, August 29, 1967.

17. Smallwood, Bichard D. , et al, "Quantitative Methods in Computer-Directed Teaching Systens."
Stanford University, Stanford, California. Defense Docunentation Center. Defense Supply
Agency, flarch 15, 1967.

18. Struma, Irene, "Use of CAI in New York State Public Schools." Summary Beport, Board of
Cooperative Educational services #1. Yorktown Heights, N.Y. October 1968.

1.9. Suppes, Patrick and Hona florningstar, "Evaluation of Three Computer- Assisted Instruction
Programs," Technical Beport, No. 142. Institute for Mathematical Studies in the Social
Sciences, Stanford University, flay 1969.

20. Zinn, Karl L., "An evaluative Beviev of Uses of Computers in Instruction Project CLUE
(Computer Learning Under Evaluation) u.S. office of Education, January 1, 1969 - January

31, 1970.

SPECIAL LISTING

1. Steiner, Wilfred J. , American Jji§to£y, Summary Cards. Ciy^l war - Present Time. Set No.
2, Visual Education Association, Inc., Dayton, Ohio.

447

444

A PRELIMINARY REPORT ON COMPUTER ASSISTED LEARNING
IN AMERICAN HISTORY COURSES AT OKLAHOMA STATE UNIVERSITY

Charles H. Dollar
Oklahoma State University
Stillwater, Oklahoma 74074
Telephone: (405) 372-6211

Introduction

Dr. Duane C. Spr iestersbach, Vice-President for Research and Dean of the Graduate College
at the University of Iowa, opened the 1970 Conference on Computers in the Undergraduate
Curricula with an address in which he called for accountability by those urging further use of
computers in higher education[ 1 ]. He suggested that the extraordinary aoaentua underlying
computer usage, which was attributed primarily to federal funding, would diminish as budgetary
constraints becaae lore acute. This situation he warned, required that advocates of the use of
computers in instruction in higher education take a hard look at how they are being used and
collect hard data that docuaent the difference, if any, they aake in what students learn and how
they learn. Toward this end. Dr. S pr iestersbach proposed a list of questions that proponents of
the use of coaputers in undergraduate instruction aust face. If the papers presented at the 1971
Conference on Coaputers in the Undergraduate Curricula accurately reflect wbut is going on in
the use of coaputers in higher education, then it is fair to say that Dr. Spriestersbach' s
exhortation has yet to be heeded se riously[ 2 ]. Accountability is still not a major concern.

This paper reports preliainary results of a prograa of conputer assisted learning in
Aaerican history courses at Oklahona State University that attenpts to cone to grips with Dr.
Spriestersbach #s call for accountability. In no way is this paper to be construed as fully
satisfying this call. Rather, it narks only a beginning. It is anticipated that the prograa at
Oklahona State University along with coaparable prograns at other institutions of higher
education will generate the data required to assess the contribution coaputers aake to
lear ning[ 3 ]•

The prograa itself, which is being funded by grants froa the National Eadowaeat for the
Hunan ities, the Gulf Oil Foundation, and the Oklahoaa State University Education and Research
Foundation, will be discussed later. At this point it is necessary to consider briefly the
development of the program.

several years ago the writer becaae interested in exploring the possibilities of using a
conputer in teaching undergraduate Aaerican history courses. A review of the then available
literature disclosed that computer usage generally consisted of drill and practice exercises,
aastery of aatheaatical foraulae and statistical techniques, and problea solving. Mone of these
applications seened particularly useful in undergraduate Aaerican history courses. Drill and
practice exercises replicate rote memorization of factual information. Most students who enroll
in American history courses have a minimal (or perhaps none) mathematical and statistical
background. Furthermore, student aastery of the course content rather than statistical
techniques for which they subsequently would have little use was a major concern. Use of a
computer in teaching undergraduate Aaerican history, therefore, seemed inappropriate.

Further study of the problem, however, suggested that this dissatisfaction was unwarranted.
Computer capability could be tailored to fit history courses rather than reshaping the courses
to conform to the computer or dismissing it as irrelevant to undergraduate American history.
Therefore, over a period of tine several guidelines for adapting conputer capability for use in
teaching undergraduate American history courses evolved. They were: (1) use of a computer must
be based on an explicit instructional strategy; (2) use of a computer must be clearly related to
the content of the course and conventional instructional techniques; (3) use of a conputer must
concentrate upon information retrieval and simple arithmetic computations; (4) use of a conputer
aust minimize student involvement in computer processing operations; and (5) use ot a computer
aust be simple and straightforward enough to be understood readily by all students in the
course.

These five guidelines were followed in constructing a series of conputer assisted learning
units for an upper division American history course. A major concern was the selection of an
explicit instructional strategy. The inquiry approach of the "New Social Studies" was chosen
because it focused upon learning rather than teaching and it emphasized the development of
critical thinking abilities in a historical context which perhaps could be enhanced through
computer technology! 4 ]. There are five steps in the inquiry approach:

Section I

449

1. defining a problea

2. developing a testable hypothesis in teras of the problea

3. selecting the appropriate data for testing the hypothesis

u. testing the hypothesis

5. evaluating the results

Bach of the coaputer assisted learning units, therefore, was structured in teras of the goals
and activities of the inquiry approach.

Bach unit was an integral part of the course and peraitted students to' exaai ne a topic in
greater depth than attempted in either the textbook or lectures. Por exanple, one unit dealt
with restrictive inaigration legislation in the 1920's. The lecture and textbook context for
this unit was intolerance in the 1920'sf of which restrictive iaaigration legislation was one
■ani f estat ion. Students could use lectures, textbook assignments, and special reading
assignments as sources for defining some aspect of the problem of restrictive immigration
legislation and developing a testable hypothesis about it. Thus, this unit, along with the other
units, was a viable part of the course content and fit in with the traditional lecture approach.

The units were designed so as to require the use of a computer to retrieve information and
to perform simple arithmetic computations. A data file appropiate for each unit was generated.
The evidence could be retrieved as raw data or aggregated, subtracted, divided, or multiplied.
One of the units focused upon voting patterns in New York, flichigan, and Nebraska from 1920
through 1940. The data file for each state contained county level units of information on some
300 variables. These variables included election returns for major elections and census
information for each county for 1920- 1930, and 1940[5). Thus, for each state there were about
20,000 separate items of information which could be retrieved or converted into another form
such as percentages. For example, in testing an hypothesis about voting behavior in the
presidential election of 1936 a student might want to compare those counties with a large
Democratic plurality with those counties whose population was largely of foreign born
extraction. Since much of the New Deal literature emphasizes the immigrant vote in that
election, a student could hypothesize that those counties with a high percentage of foreign
born stock would also be those counties with large Democratic pluralities.

Early in the developmental stage it became apparent that few students could be expected to
submit a unique computer run which retrieved the desired information and performed specified
computations. Accordingly, student involvement in computer processing operations was minimized
by making available a complete listing of the raw data and all possible computations. This
usually resulted in inundating students with information for which they had little use. However,
in comparison to the problems encountered with each student attempting to submit a unique
computer run, this inconvenience was minor*

The fifth guideline followed in developing computer assisted learning units was simplicity.
Learning activity packages were derigned which permitted each student to complete a unit at his
desired pace (within certain limits, of course) with minimal dependence upon the instructor.
Included in each package was a flow chart of required activities, student performance
objectives, a review of the inquiry approach, a description of each variable in the data file,
and an explanation of how to interpret the computer output. This emphasis upon simplicity did
not confine students to simpleminded questions and problems. On the contrary, each learning
activity package had an open-ended structure which encouraged students to develop and test
significant hypotheses.

Section II

In the Spring of 1970 the Oklahoma State University Computer Center made available time-
sharing conversational capability to the campus. This on-line interactive system, which is run
under IBH's Conversational Programming System (CPS) [6], permits students to access data files
via remote terminals and to retrieve information or to perform specified calculations. With the
support of the National Endowment for the Humanities and the Gulf Oil Foundation the existing
computer assisted learning units were converted to CPS and new units begun. A two year program
was commenced which would: (1) measure the effectiveness of the "inquiry approach," supported by
computer technology, in enhancing critical thinking abilities; (2) disclose students'
perceptions of the function of computers in the instructional process without regard to
discipline; and (3) determine the relative cost per student of offering this kind of learning
environment. The balance of the paper describes the current status of the program and reports
preliminary results regarding costs and students' perceptions. In addition, it documents some
error and mistakes.

There are now six operational computer assisted learning units being employed in three
American history courses at Oklahoma State University. The first of these, which is called RCVA
for Boll Call Vote Analyzer, provides an on-line retrieval capability for the analysis of
senatorial roll call votes[7]. The data file for RCVA will accommodate 100 senators' responses

44650

of yea and nay to 25 roll call votes. The retrieval phase of RCVA offers students sevas nodes of
access to the roll call votes. They are:

1. List a group of senators' responses to a particular roll call
vote.

2. List a group of roll call responses aade by a particular senator,

i. List a group of roll call responses aade by the senators froa a

particular state.

4. List the rav and percentage results of a particular roll call vote
by party division.

5. List the rav and percentage results of a particular roll call vote
by region.

6. List the Index of Cohesion for each party for a single roll call
vote.

7. List the Index of Cohesion for each region for a single roll call
vote.

Students select one of seven nodes of retrieval in response to the instruction: SBLSCT TOUR

OPTION. One ot the seven possible responses listed belov vhich correspond to the seven nodes
given above, is typed in.

1. LHC

2. LSEN

3. LSTATE

4. JPARTY

5. ftREG

6. CPARTY

7. CREG

Aa exaaple of the LRC option is shove in Figure 1. RCVA also aaintains a file for each student
vhich records hov nany tines he has used the systen[8]» RCVA is currently being used to access
the 21 roll call votes dealing vith restrictive iaaigration legislation nentioned earlier as
veil as civil rights legislation in the 1950*s and t960's. Thus, there are tvo RCVA units for
tvo different tine periods.

The third coaputer assisted learning unit is VOTRAN, vhich is an abbreviation for Vote
Analyzer. VOTRAN provides an on-line retrieval capability for the analysis of election returns
and census data. The data files contain the infornation for Mev York, flichigan, and lebrasha
described earlier in this paper. Students say select the state to be analyzed and then exercise
a series of options vhich include:

1. List rav data for one or nore counties on a particular variable.

2. Conpute and print the percentage of a county's or a group of
counties' total of the state total for a selected variable.

3. List the total of a variable for tvo or nore counties on a
selected variable.

4. List the state's total for any nunber of variables.

5. Rank any nunber of counties on a single variable and print out
the rank order of all the counties or print out a selected nunber
fron the top, niddle, and botton counties.

6. Aggregate, divide, subtract, or nultiply tvo or nore variables.

The instructions for executing the options are:

1. Rov or r

2. Percent or %

3. Ctotal or c

4. Stotal or s

5. Rank

find or f
list or 1
top or t
niddle or •
botton or b
6- 7, ♦, /, or *

Figure 2 illustrates hov a student used VOTRAN options 3, 4, 5, and 6 to access the Rev
York data file. In this exasple the top five and botton five counties on variable 71, the
percentage Oenocratic vote for President in 1928, vere retrieved through the rank option. These
ten counties (the nuneric code for each county is given in the learning activity package) vere
then ranked on variable 241, the percentage nonvhite in 1930, variable 247, the percentage urban

44 7

ERIC

451*/' •

Select your option.

rr.nk

Vhlch variable?
v*r

►

Select your option.
LTC

Which ecnaior?

Cura

Which roll cella?
*11

Vhlch counties?

1-62

One taODCnt pleas*.
Vhat -would you like?
top

Eov &any?
cun

&ENATC2 37

TS)\X CA?,L

6
7

20
21

response

YEA

ABSENT

KAY

YEA

KAY

YEA

KAY

YEA

KAY

/as ENT
ABSENT

YFA

YEA

ASSENT

ABSENT

Ai) $ EN i

YEA

ABSENT

kank

County

Date

6C.3CO

61. ICO

39. SCO

50.000

S3. C00

Vhat would

you like?

bottom

Bov many?

nua

Bank

County

Data

22.000

21.400

21.100

20.700

18.000

Select your option.

rank

Which variable?
var

241

Vhlch counties?

3,31,24, 10,1, 9. 54,13,62, 2

.;»rL

Variable

FIGURE 1

FIGURE 2

One cocent plecsa.
What vould you like?

Tiet

✓

Emk

County

Data

12.600

2 .SCO

1.300

1.100

1.000

.600

.500

.vv>

• 3'X>

Select

your option.

reuk

Which variable?

var

247

Which counties?

3,31,24

.10.1.?. $4.13.

62,2

One cosent pleacc.

What vould you like?

lift

Sank

County

Data

99.600

99.8CO

99.600

80.700

40.600

35.600

31.600

24.200

14. $00

f.SOO

Variable

Variable*

What vould you likat

Select your option.

rank

Which variable?

var

243

phich counties?

FIGURE 2. Continued

449

OPINION

ANALYSIS OF PUBLIC
What Is your Identification number?

If)

This Is session 1 for you*

What survey do you want to Investigate*

1304

In a moment you will compare the responses to any two
questions selected from the list In your packet* After
you specify which two questions are to be compared a
frequency table for that pair of questions will be typed
out. Then you wl 1 1 he asked If you want to sea tabla
percentages, column percentages, and row percentages*
if you wish to sec this Information Just answer yes or
no to the questions. Remember that you can compare only
two questions at a time*

Type the number of the first question under the label varl
and the number of the second question under the label var2«

What are the numbers of the two questions you want me to compare?
varl

var2

Table of Frequencies for Question 2 and Question 24
Row-Question 2 Column-Question 24

Row/

4 Total

1 141 |

15 7 |

41 1

12 1 351 |

1 138 |

249 |

92 |

14 I 493 |

1 115 |

165 |

195 |

5 1 480 |

1 97 |

115 |

24 |

11 I 247 |

Total

1 491 |

686 |

352 |

42 r 15 71 |

Do you

want to see

table i

percentages?

Table

Percentages for Question 2 and Questl*

Rovy-Ques t Ion

Colunn-Questlon

Row

4 Total

1 9.0|

10.01

2.6|

.81 22.31

1 8.8|

15.81

5.9 1

.9| 31.41

1 7.3|

10.51

12.41

.31 30.61

1 6.2|

» “in 7i

7.31

1.51

.71 15.7|

FIGURE 3.

454

450

in 19J0, and variable 243, the percentage foreign born stock in 1930. The object in ranking the
counties on these variables was to determine if there was any significant shift in rank from
that on variable 71, the percentage Democratic vote for President in 1928. The Ctotal or c
option was then used to aggregate variable 65, the Democratic raw vote for President in 1928,
for the top five counties on variable 71. Next, the Stotal option was used to retrieve the total
state Democratic raw vote for President in 1928. The 7 option then yielded the percentage the
five county total was of the total state vote.

APO, or Analysis of Public Opinion, is the fourth computer assisted learning unit now oeing
used to teach American history at the undergraduate level. Like the other units described
previously APO is an on-line interactive systen which pernits students to access and nanipulate
data files composed of responses of a representative sample of the adult population interviewed
by the Survey Research Center of the University of flichigan in 1960, 1964, 1968, and 1970191-
Data file manipulation consists of cotparing responses to a selected pair of questions and
printing out a cross-tabulation frequency table, table percentages, row percentages, and column
percent ages.

The current APO data files include responses to between 45 and 55 questions selected from
about 450 questions asked in each survey because they involve contemporary social and political
problems of great interest. For example, several questions measure attitudes toward segregation
and desegregation and civil rights activities of Blacks while other questions deal with American
involvement in Vietnam.

Figure 3 displays the options available to students in APO. The 1968 survey was selected
and a comparison of the responses to questions 1 and 55 was requesteu. Question 1 deals with the
population of the place in which the respondent lived while question 55 asks how he voted for
president. The table printed out lists how the respondents voted by population. Population areas
are indicated by the row numbers at the left and vote for president is indicated by the column
numbers at the top of the table. (The learning activity package for this unit explains what each
row number and column number means.) Execution of the table percentage and column percentage
options yielded the two other tables in Figure 3.

A more sophisticated version of APO is called TDAPO or Third Dimensional Analysis of Public
Opinion. It uses the same data files as those in APO but compares responses to a pair of
questions while controlling for a third question. Suppose, for example, a student wanted to know
if southern women were more intolerant toward desegregation than were their counterparts in the
North, the Midwest, or the West. The responses to questions of the region in which respondemts
lived and their attitudes toward desegregation would be compared while controlling for the
question of sex. TDAPO would print out two cross-tabulation tables, one for female and one for
male. Each table or plane would be broken down by region and attitude toward desegregation.

The sixth and last operational computet assisted learning unit is called Ghetto[10J. It is
a computerized version of the educational game Ghetto which is a simulation of what life is like
in the ghetto. It is designed to expose non-ghetto residents to some of the pressures at work in
the inner city neighborhood. Each player selects one of ten roles of poor people and tries to
improve that person's life. In this attempt he experiences vicariously some of the frustrations
and deprivations that affect the lives of the urban poor.

Unlike the board game, the computerized version of Ghetto requires only one player. A
player selects a profile and then describes himself to the computer in terms of responses to
questions such as how old he is, how many children he has, what is his level of education, what
is his sex, and how many hours b. has to invest. (All of this information is given in the
learning activity package of this unit.) After this description is typed in, a player then is
asked how he wants to invest his hours. He nay elect to invest his hours in school, work,
hustling, recreation, and welfare. Since the object of the game is to score as many points as
possible during ten rounds, a player normally makes an investment that beings the greatest
number of points. Hustling, and especially big time hustling, offer great rewards but also run
the risk of arrest. On the other hand, education offers great opportunities to improve future
earning power and thereby earn more points.

Built into the computerized version of Ghetto are chance factors over which a player has no
control. Illness, for example, is assigned by a random number generator. Pay cuts, being robbed,
or being ‘ arrested if you hustle are also assigned on a random number basis. Each female runs a
16 percent chance of having a child, again on a randon number basis.

A round is completed when an investment is made and the chance factors are generated. The
computer totals thp number of points earned. The sequence is repeated until ten rounds have been
played and a total score is tabulated.

Thus far Ghetto has been played by pairs of players who select the same profile. The first
player moves through the game following one strategy. The second player plays the game using
another strategy. For example, the first player eight concentrate upon hustling while the second

455

451

player focuses upon work or
This tends to reinforce
mobility, it is exceedingly
the largest reward.

education. At the conclusion of the
the lesson that while education
difficult to do this in the inner ci

game they could compare resalts.

usually is a vehicle for apward
ty. Hustling generally provides

Each of these units is operational and has been tested in one or more of the following
history courses at Oklahoma state University: History 4503, The American City Since 1865, if a
ju n i or- senior level course; History 2493, American History Since 1865, is a freshman-sophomore
level course; and History 4183, American History Since 1920, is a junior-senior level course.
Student participation in testis these units was voluntary, although in the two upper division
courses students were strongly encouraged to participate. In the Spring senester of 1972,
students enrolled in History 4183 will be required to complete these six units plus two others
now being developed. Student participation in History 2493 in the Spring senester will continue
to be on a voluntary basis.

Section III

At this point in the paper attention can be directed to two major questions: (1) What was

the cost of using these six units? (2) How did students respond to conputer assisted learning?
The first question can be readily answered and with considerable accuracy. Table I summarizes
what is called developmental costs. Included in the table is a unit called IVIS which was
dropped after having been developed to the point of being operational. Excluding this unit, the
cost of programming, CPU, and data file creation was $2,335.00. Almost one-half of this ($1,000)
is accounted tor oy creation of the APO files of 1960-1970. There are several reasons for this,
one of which is that considerable recoding of the survey data is necessary, flore important,
however, is that each file contains cross- ta bulat ions of the responses to each question with
every other question (there are 1486 such cross- tabu la ti ons) with answer codes that range trcs 1
to 10. Of course this is a one time expenditure.

Unit

Program! ingf a ]

CPU

Creation

RCVAI

$125. 00

$ 25.00

—

RCVAII

25.00

10.00

—

Votran

150.00

50.00

$ 200.00

ivis[ b]

145.00

200.00

—

APO

225.00

150.00

1 000. 00[C]

TDAPO

100. 00

50.00

125.00

Ghetto

7 5. 00

25.00

—

Totals

$700. 00

$310.00

$1325. 00

[a]

not included

in totals

[b]

prog ra mming

charge is $5.00 per hour

[c]

this include

s five separate files whi^h

initially are created in the

batch processing system

at a cost of $200.00 per file

Table II displays a report of approximate instructional costs of using four of the six
units in an actual teaching situation. Inspection of the table discloses that with the exception
of Ghetto, Votran, APO, and TDAPO are quite costly, although this can be reduced by increasing

the number of users. The TDAPO unit costs more per student simply because of the extensive

computer sorting that is necessary in controlling for a third variable. On the average about two
minutes of CPU ($100 per hour) are required to generate one comparison. Thi* in turn translates
' into about fifteen minutes of elapsed terminal time ($1.80 per hour), notice that there is only
) a difference of $1.79 per student between lower division and upper division users. This is not
was much as one night expect, given the fact that there were four more users in History 4503. A
? comparison of the mean CPU and mean terminal time for the two groups discloses that students in

' History 450J used on the average almost one minute more of CPU during almost the same average

i terminal time. This suggests that junior and senior students made much more efficient use of
terminal time. Also, a comparison of the hypotheses the two groups tested indicates that on the
whole students in History 4503 were much more complex.

The APO unit instructional costs vary considerably. The cost per student user in History
4503 was $8.54 during the summer and 12.79 in the fall. The lower cost is explained by the fact
that only two survey data files were available during the summer and that students during the
fall averaged one minute and twenty seconds more of CPU and twenty minutes more of terminal

453

tile . This suggests that students in History 4503 during the Pali semester posed hypotheses
that required more elaborate data retrieval. When the cost per stu< dleot figure for History 45QJ
and History 2493 is examined, the forier is aliost twice as high. The larger number of users
(22 as opposed to 10) in History 2493 helps to account for this along with the fact that upper

division students tended to sake more affective use of terainal tiae. Despite this, the cost per

student is still quite high. The explanation for this is the five IPO data files are enormous,
occupying in excess of 550 disk tracks at a cost of $5.50 per day for data and systea storage.
a

Votran is a rather expensive unit also. Interestingly enough, the major cost of Votran is
CPU tiae. There are two reasons for thus. First, twice as aany students used Yotran as used IPO
or TDAPO. Second, the rank option is this unit siaply /requires extensive sorting which uses
considerable CPU tine. It might be noted also th*t after the rank option is executed, about five
minutes of terainal tine (this varies with the nunber of terainal users) elapse before any
information is * ped out.

A review of the conputer aspects of Votran, APO, and TDAPO indicates that the cost per
student can be reduced somewhat. If the one-line rank option of Votran is eliainated, this
would likely cut the cost in half. In order to do this a new data file will be created in which

every variable is stored botl ;n raa'v order a*\d in natural order. This will increase the si'*e of

the data file by about one-third with increased storage costs, but this will be lore thaa offset
by sharply reduced CPU time. The cost of APO can be lowered by shortening the aaount of tiae
that the system is up. Probably a limiting access to APO to twenty-one days (the inforaation in
Table II is based on thirty days) students will encounter no difficulty. However, a period of
tiae less than this night ceate hardships for soae students. TDAPO cost per student can be
reduced by having students use the renote job entry (RJE) feature of CPS to enter a job into the
batch processing stream. The print out nay be picked up several hours later at the Conputer
Center. There is some question as to whether reduction in cost will not offset the inconvenience
of waiting several hours to analyze the data.

Reference was nade earlier to IVIS, a unit that was dropped. Proa a programing point of
view IVIS was quite elegant, chiefly because of its remote job entry (BJE) capability which
permitted students to enter a job in the batch stream from a remote terminal with three simple
executions. Despite its elegance, however, IVIS was dropped because test runs indicated that the
kind of jobs processed in this way would cost in excess of S30.00 for each job. There was no way
to justify this in a class of thirty students. Therefore, IVIS was relegated to the junkplle of
impractical projects. It was an expensive lesson, but one well learned. It night be noted in
passing that IVIS was not a total loss. The remote job entry (BJE) of IVIS can be added to TDAPO
with a few modifications, although it too nay prove impractical.

Earlier in this section of the paper two questions were posed, one of which dealt with
costs and the other with how students responded to the computer assisted learning units. The
cost factors have been discussed. Attention nay now focus upon the responses of nineteen
students in History 4503 to a survey of their attitudes toward conputer assisted learning. The
following statements summarize the results of this elementary survey.

1. Only one student indicated that computer assisted learning was not

useful.

2. Interestingly, ten students considered the four conputer assisted
learning units less difficult thar* conventional textbook assignments
of comparable duration. One student noted that the units were less
difficult because "you can see what you#re doing."

3. In terms of preference for the four coaputer assisted learning units
one student had no preference (this was the same student who considered
computer assisted learning not useful), three students preferred
Votran, five favored APO, five chose TDAPO, and six selected Ghetto.

4. Only two of the students indicated they were not uncomfortable and ill
at ease when they first used the terminal. Both of these students had
had previous experience in using a remote terminal.

5. Fifteen of the students reported that by coapletiott of the second unit
they were no longer uncomfortable or ill at ease.

6. when asked if they could choose between enrolling in a class taught
without computer assisted learning units and a class taught with these
units, fifteen <;aid they would enroll in the latter. Several students
added the comment that a course utilizing computer assisted learning
units would be more interesting and enjoyable.

Additional student feedback disclosed that the two class sessions devoted to briefing students
to tho units and how the remote terminal works were insufficient. It was the consensus of the
group that they felt like a non-swimmer who had been taught to swim by being thrown into a body
of Water and told to swim, flore attention must be given to tnis problem as well as to urging
students to be less impatient while awaiting completion of a rank option or a TDAPO execution.

453

457

Apparently, a nuiber ot students were bored by this aspect of a five or ten ainute delay la the
inforaation being typed out.

An appropriate note on which to conclude this paper is that of observing that this paper
reports findings that only point toward the hind of accountability required. Bore inforaation on
costs and student attitudes is essential. In addition, differences that conpater assisted
learning lakes in what students learn and how they learn aust be docuaented. The project at
Oklahona State University will atteapt to provide soae of this inforaation and docaaen tatioa. In
the Spring semester of 1972 a total of eight coaputer assisted learning units trill be used in
History 4183 and History 2493. A pproxiaatel y 75 students will be involved. Also students in
History 4183 will participate in an evaluation of the effectiveness of coaputer assisted
learning in enhancing critical thinking abilities. The hypothesis to be tested is that studeats
a exposed to coaputer assisted learning as described ±n this paper will register improvement in

critical thinking abilities. A pretest and posttest using the Watson-Gl azier Test of Critical
Thinking will aeasure this iaproveaent. Obviously, this will be a very crude measure since there
are too aany uncontrolled variables which night intervene. However, in both the fall of 1972 and
the Spring of 1973, one class in Aaerican history will be taught using conventional classrooa
instructional approaches and another class (the saae course) will use the coaputer assisted
learning units described in this paper. It is anticipated that by using an experimental class
and a control class the results will have greater validity.

FOOTNOTES

1. Proceedings, Conference on Coaputers in the Undergraduate Curricula, 1970 (University of

Iowa) , pp. 0. 1* )m 3.

2. Proceedings, Conference on Coapu ters in the Undergraduate Curricula. 1971 (Dartaouth

College) •

3. For exaaple, the National Science Foundation is supporting JBDUCOH's "Investigation of

Factors That Inhibit Widespread Use of Coaputers in the Instructional Process."

4. Edwin Fenton, The New Social Studies (New York, 1967), pp. 6-27.

5. This inforaation in aachine readable fora was obtained froa the Historical Archives of the

Inter-University Consortium for Political Besearch, University of Michigan, Ann Arbor,
Michigan.

6. CPS stands for IBM 1 s Conversational Programming System and is a tine-sharing node of

coaputer-user interaction.

7. These two units have been tested and are operational. However, they are not included in

cost analysis later because their substantive content deals with a course taught in the
Spring of 1971.

8. Certain constraints of CPS Bake it difficult to obtain a record of the actual amount of

CPU and terainal time used. Students turn in the last page of their typed output which
includes a record of CPU and terainal tine. Sometimes, students lose this piece of paper or
forget to turn it in. This particular feature of recording how aany tiaes each student uses
the systea (each student has a separate identification nuaber) will disclose any
discrepancy between actual student perforaance and the inforaation he turns in.

9 . This inforaation in machine readable foraat was obtained froa the Survey Besearch Archives
◦f the Inter-University Consortiua for Political Besearch, University of Michigan, Ann
Arbor, Michigan.

10. I am grateful to Academic Gaaes Associates, Inc. for granting ae permission to develop a
computerized version of Ghetto.

ERIC

454

458

EDUCATIONAL OSES Or

msi!

Hilliaa D. Copiin
Nichael K. O'Leary
Syracuse University
Syracuse* Rev Tort 13210

l PRINCE* ■ progranned international relations computer environaent, operates as a nan-
conputer sieulation in which the student plays the United States foreign policy-iaker and the
coeptiter plays five other states as veil as doaestic political pressures within the United
States. It also operates as an all-conputer sieulation aodeling international political
processes* PRINCE serves as an educational tool with a vide variety of applications. The

categories of uses discussed belov are not autually exclusive. Two or three educational
applications night be pursued siaultaneously which nay* in fact* be the nost desirable way to
proceed in nany educational settings. Ve hope* hovever* to suggest a list of the full range of
educational uses that night be nade of PRINCE as it currently operates.

As ?in educational tool* PRINCE can help achieve five general goals:

1. Introducing the student to basic facts about conteaporary international relations;

2. Providing the student with a f ranework for understanding those facts;

3. Intioducing social sgienge net hods and inforning the student of cor rent theory g£d
£*££&££& in international relations;

4. In proving the student's dgci^ian-nakiaa planning stills;

5. Helping the student to deal with the probleas of effectively 2£2£BiiifiS § 3£2!AE
undertake coaplex decision-naking.

Each of these uses will be briefly described below.

It\ty3 <|ttS£jos to the Pacts of Contgfpogapy lBte£M£i2B£l Rel^jjons

At its least coaplicated level* PRINCE can be used as a vehicle to get the student to learn
and digest basic facts of the conteaporary vorld. The aodel is regularly kept up to date so that
any play starts with the present international situation and extends into the iaaediate future*
A student who plays the aodel in Septeaber* for exaaple* vill be asked to Bake policy regarding
the issues which are current at that tine* The student can be asked to study newspapers and
other periodicals to deteraine the state of those issues being dealt with as preparation for
aaking appropriate decisions in the sieulation* A perfunctory reading of the Rev Tg£k Tiees will
not suffice* The student will be encouraged - and* on the basis of our experience* actually
aotivated - to seek out infornation with as such* if not nojre* enthusiasm as the Foreign Service
Officer does evory norning of his life.

This use of PRINCE is the nost direct and least coaplicated of the six uses. It can be
successfully achieved vith as few as three cycles of the PRINCE aodel and two weeks of a regular
three-hour course. At Syracuse University* the Political Science Departnent has prepared a one
credit "nini-course," entitled 11 The United States in Vorld Affairs*19 which is open to all
undergraduates. The students are divided into teaas of four. Each tean is asked to brief itself
on a particular set of issues and countries in the aodel and to play six cycles. Resources
available to help the students prepare theaselves for play include tape-slide presentations
describing the foreign and doaestic politics of states* extensive newspaper clipping files* and
a bibliography. After six cycles* the students subsit a report on their policies and their
analysis of the results of their "tenure in office*"

In this particular educational node* PRINCE is being used prinarily to provide an
intriguing environaent within which students vill systenatically study substantive facts about
conteaporary international relations. Such use would be nost appropriate in general college
courses and perhaps even high school courses dealing with either United States Foreign policy or
International Relations. It can be organized as a short course on its own* or included in a
full-tera coarse. Because its educational objectives are focused on the acquisition of basic
infornation* this use of PRINCE night also be appropriate for high school courses as well as
adult education.

459

A P oe wo£k £or ^nder st^gd^nq International

Relations

In addition to providing a context to motivate students to acquire the tacts o£
international relations, PRINCE can also be used as a Beans for helping the student acguire a
basic conceptual framework. In this case, the educational aia is not to help the student acquire
information about conteiporary international issues, but rather to provide hii with a set of
concepts that will help hin like sense out of the inforaation available to hia. Basic concepts
like international bargaining, diploaatic pressure, transaction flows, and doaestic political
influencers are introduced to the participant as he attempts to deal with the simulated
international environaent. Aftar playing the exercise a number of cycles, the student should be
able to describe international relations in terms of these and other related basic concepts.

This use of PRINCE requires on
which the basic concepts are related
commentators and to the events a
asked to describe the Middle East Pr
and domestic political infliences
suggestions of a writer like Henry K
PRINCE is typically employe! in
policy. It provides an alternative t
through textbooks or lectures. I
which are supplied in the traditiona

ly a few cycles of play followed by a thorough discussion in
to the writings of international relations scholars and
s reported by scholars and journalists. The student night be
oblen in terns of sets of issue positions among the states
within states, or he might be required to relate the policy
issinger or Thomas Schelling to the PRINCE world. The use of
introductory courses on international relations or foreign

0 the normal procedure of providing a theoretical framework
t can, of course, be used to supplement and compare concepts

1 fashion.

An Introduction to Social Science Ijethod and Literature in £he Study of International Relations

A third and more complex use of PRINCE is to provide the student with an introduction to
the methodological and theoretical problems involved in the social scientific study of
international relations. Aftar learning the basic PRINCE concepts through playing a few cycles
of the simulation, the student is then introduced to the concepts and theory of which the
computer model is composed. In addition to the concepts visible to the player (e.g. , issue
position, influence attempts, transactions and domestic political influencers), there are other
concepts such as affect, salience and power that form the theoretical infrastructure of the
model. Additional ideas such as dependence, the irresponsibility ratio, and the reference ratio,
which are derived from the basic concepts of issue position, power, salience and affect are also
described. The student is provided with both verbal and written descriptions of the concepts and
theories in the model.

In the context of this description, the student is then provided with the opportunity to
work on a variety of problems. First, and at the most general level, he can see tho utility as
well as the limitations of xodels in the study of international relations. Second, he becomes
aware of the challenge that must be faced in testing the validity of the theoretical ideas in
the model. The tasks involved include collecting data from appropriate sources, selecting
correct measurement techniques, and relating existing theoretical and research concepts to the
operations in the model, and the choice of appropriate statistical techniques for testing the
relationships between variables. Third, he can start to test some of those ideas himself and
suggest alterations in the basic model based on the ideas of other scholars as well as his own
thinking. From the perspective of the PRINCE model, the student can be introduced to advanced
and sophisticated approaches to the social scientific study of international relations.

Our experience suggests tha
who have had some previous worn
graduate students have been
international relations through
model for failing to conform to
theoretical relationships using
task, the model can be util
past, we have found that up to e
profitably be used in these task
three-credit course will be buil

t this use of PRINCE is best reserved for more advanced students
in international relations. Juniors, Seniors and beginning
introduced to the research and theoretical literature on
this approach. They have critiqued particular aspects of the
the theories of scholars and have tested the validity of certain
data from a variety of sources. Given the complexity of the
ized in this mode for a substantial period of class time. In the
ight or ten weeks of a normal three-credit advanced coarse can
s. When supporting analytical materials are developed, an entire
t around these activities.

Providing the Student with the Opportunity to Improve His Decision- Making and flanging Skills

This use of PRINCE shifts from providing inforaation, a framework or an approach tor
understanding other scholar's framework to helping the participant to be able to handle better
decision-making under complex and uncertain conditions. PRINCE represents a highly complex
environment in which the player must learn to deal with a large amount of information which
often appears at first to have no discernible pattern. He also is confronted with an environaent
where multiple and often competing goals are suggested.

the

(5)

The player must learn to deal with the five classic tasks
situation, (2) selecting goals, (3) examining alternatives,
determining the consequences of decisions. Evaluating the

of decision-making: (1) defining
(4) choosing alternatives and
skill with which these tasks are

45£

460

performed can best be done in the context of a dynamic and complex siaulated enficonaent which
can be repeated indefinitely. The player learns the necessity of developing explicit aodels
about the world that can be continuously checked and readjusted. He sees the value in Baking his
goals explicit so that he can leternine what information is iaportant to hie and what is not. He
can explore a variety of strategies so that he can learn to project the consequences of
alternatives. And finally, he is given practice in eating choices in a coaplex environeent where
only the bare outlines of the probabilities can be ascertained*

This use of PRINCE can be undertaken in a variety of educational contexts. Host students
are eager to try their hand at decision-eating; PRINCE can provide hie with a surrogate
environaent which is iaaediately challenging and yet coaplex enough to warrant aore thoughtful
analysis. Similarly, aid-career training in a number of fields has cone increasingly to
emphasize the developaent of decision-aaking and planning skills. The PRINCE environeent
provides the kind of tool that the aid-career professional can use in learning to sake coaplex
decisions with uncertain inforaation. tike the college student, he can be shown the benefit of
developing intellectual guesses formalized in tentative aodels to deal with decision and
planning probleas. At the college, graduate or aid-career levels, however, the student should
be allowed at least eight cyclas of play so that he can learn to deal with sequential and fairly
long-range consequences of policy decisions. He should also be taught to develop and apply
criteria for judging the efficacy of such policies through a series of aapping and analytical
exercises.

Problems of Organization in Dealing with Complex Decision-Making and Planning

A special problem which should not be overlooked in group decision-making and planning is
the need for specialization, divisions of labor, and communications. How should a group organize
itself to deal with a complex environaent? This question is critical to the success of either
understanding or dealing with contemporary political and social decision-making. PRINCE can be
used as a source of a complex decisional task around which group structures can be built. Pive
to ten individuals can be organized with geographical and/or functional responsibilities to deal
with the PRINCE environment. In addition, roles such as information gathering, synthesis, policy
advocacy and even evaluation can be developed and introduced as part of the group structure.

This is a particularly appropriate use in the study of the politics of decision-making in
large-scale organizations. It fits well into advanced undergraduate and graduate courses as well
as in aid-career education. It exposes the participant to the problems of coordinating and
controlling members of a bureaucracy as they seek to deal with a complex environment. He
recommend that at least tei cycles be undertaken since a relatively substantial history of
relationships must develop in order to have the organizational factors take effect. Again, a
substantial part of a course or a two or three week period of intensive work is required. At the
end of that time, the writings of organizational theories can be tested by the experience of the
group as well as skill and knowledge in handling the roles of decision-making in complex
organizations.

He have briefly addressed the various uses of PRINCE in a variety of educational settings.
As we have already noted, it should be clear that more than one use can be made of PRINCE at one
time. It should also be clear that different educational uses should be applied to different
types of students. The college freshman would not benefit from learning about decision-making in
coaplex organizations via PRINCE while the mid-career professional does not need PRINCE to help
motivate him to read the newspaper* Nevertheless, the educational objectives of instructors at
virtually every level of sophistication can employ PRINCE in a useful manner.

To help carry out these objectives we have begun the development of a wide range of multi-
media educational materials. Central to all the objectives mentioned is the Participants* Guide
to PHINCE: Concepts, Environments, Procedures which is available for distribution. It is
periodically brought up to date as issues change in the international environment. The Guide
outlines the basic domestic and international environment with which the player must deal,
details the alternative policy actions available to him, and describes the basic procedures to
be followed in operating the simulation.

Video tapes and newspaper files have also been prepared to provide "country briefings" for
the student who is playing PRINCE within the context of acquiring basic information about
contemporary international affairs. A series of analysis forms is being field tested at this
time by which the student can record and study the history of his own policies and the
consequences of his actions. The tapes, files and forms will be available for distribution in
the fall of 1972.

Sum nary

Raterials are also being developed to aid the student in understanding the theoretical
structure of the PRINCE sodel. I draft version of the description of the sodel is now available
("A Brief Description of the PRINCE Model") and a final revision will be available in June,
1972* To supplenent this description, willias D. Coplin and Michael K. O'Leary will publish is
the Spring of 1972 a booh entitled "filSEXtiftlfi A Culda Understanding Iog£ Eglitkfiii
££2kl&a2" (Belsont, California; Duxbury Press, A Subsidiary of Wadsworth Publishing Coapany).
This book introduces the bisic PRINCE concepts in the context of faniliar donestic and
international political situations. In addition to the Description and El££liAAll ££Ift£&r *
Workbook is now being developed that relates enpirical data and historical case studies to the
various concepts and theories in PRINCE. This Workbook will be in draft forn by Septenber, 1972
and will provide sufficient naterial so that an entire three-credit course can be provided to
the student as independent study.

The following naterials related to PRINCE are available as of January 1, 1972 fron the
International Relations Progran, Syracuse University, 752 Constock Avenue, Syracuse, New Tork
13210s

MThe PRINCE Project and tia International Relations Prograa," this short paper outlines the
basic research and educational goals that constitute the activities of the International
Relations Prograa and PRINCE.

E SINCE Participant's Guyg; Concepts, £avi£2a§ga£g, Procedures by williaa D. coplin,
Stephen L. Rills and flichael K. O'Leary. Single orders sent upon reguest; Bulk Orders 75
cents each.

"A Description of the PRINCE Model" (SI. 50 each)

B£££I*§ai§ ££!£££* A SikiE £2 SiadStSkandifla Isai £°ikkk£&l EtaklSfs (Obtain froa Wadsworth
Publishing Coepany, Belaont, California after April, 1972).

VOTER

1 A SOCIAL SCIENCE DATA ANALYSIS PROGRAM

Bruce D. Bowen and Bayne K. Davis
The University of Michigan
Ann Arbor, Michigan 48104
’ Telephone: (313) 764-0327

Iu Product ion

VOTER is an example of an instructional use of the computer which accomplishes educational
objectives probably not possible by any other leans. The VOTER program was written for use at a
remote terminal for the unsophisticated student user to develop his ability to analyze and
interpret large sets of data. The program has been specifically designed to be used in
undergraduate political science courses. This paper will describe two different uses of VOTER
in these courses.

VOTER has been designed to achieve the following instructional objectives:

1. to enhance the student's understanding of the theory, practice and use of survey
statistics through direct involvement with real data bases;

2. to encourage the development of those intellectual anilities required oy the process
of uncovering and interpreting information which is effectively new;

J. to provide direct contact with a computer, at a level which is appropriate given the
student's background and needs, in a worthwhile enrichment experience.

VOTER can ne used by the instructor as a stimulus for discussion, a device to motivate and
facilitate individual study, a source of factual content for course work, or a research tool for
project-oriented assignments on an individual or group basis. The cost of using the program is
minimal; its educational value to the students are largely a function of how it is used by the
individual instructor and student.

Description of tne Program

VOTER is designed to generate labeled, univariate and bivariate frequency tables selected
by the student. VOTER is data ba se-independe nt since practically any data base can be prepared
as input, and routines have been written to prepare new data sets tor analysis by the VOTER
program. The program provides for selecting samples and subsets of the data base that has been
entered. In addition to producing univariate and bivariate frequency tables, VOTER also computes
correlational statistics to accompany tables selected by the student.

At different points in the program the student can select samples or subsets and determine
the type of table or statistic to be computed. One way to describe the operation of the program

is to explain the options available to the student at each point in the program's execution. An

attempt will be made to describe these options as the typical student works his way through the
program.

After initiating the VOTER program, the first option open to the student is the selection
of a sample of the data with which he wishes to work. The option consists either of the entire

sample or some sunset of the sample. If the student selects the entire sample he is given

another option. This option consists of naming a column variable. If the student selects a
sunset of the entire sample, the selection of a column variable is postponed until the subset is
identified. Naming the column variable is accomplished by entering a variable name which not
only selects the column variable but also retrieves the stored labels that will be printed with
the table. Alter selecting the column variable by name, the student has the option either of
entering the name of the row variable for a bivariate table or entering "none1* to indicate that
he would like a univariate table.

If the student enters a row variable he is next asked to determine the independent
variable. The selection is important for two reasons. First of all, the percentages that are
printed with the frequencies in the* table are given in terms of the independent variable. It
for example, the student indicated that the row variable was the independent variable the
percents would be given so that each row of percentages would sum to 100. If the student
identified the column variable to be the independent variable, each column of percentages would
sum to 100. The student may also select "total" which would cause the percentages to be
computed so that the sum of all percentages ir. the table would be 100. Secondly, naning the
independent variable insures the calculation of the proper asymmetric statistics. After the
table has been printed by the computer, the correlational statirtics are given to help the

463

459

student in the interpretation of the table. These statistics are Kendall's tau, Ganna, Somer's
D , and Goodaian and Kruskal's Lambda.

After the statistics for the table hate been printed, the student is allowed to sake
another choice. This choice is either to (a) start again with the entire sample, or (b)
continue generating tables with the existing saaple or subset as he has already described it, or
(c) make additions or deletions to the current saaple (or subset) using the filter procedure.
Also at this point or any other option point in the program the student nay enter "stop" and the
program will terminate. if the student would like to do filtering, he would enter the response
"more” indicating that he wishes to enter a filter command.

The filter command consists of three pieces of infornations the variable name, either the
keyword "include** or "reject”, and the response code nnmber. If he types "reject", all cases
with the code number specified will be deleted froa the saaple. It he types "include," all
cases with the specified code nuaber will be included in the saaple along with any other capes
that have not been explicitly deleted.

The student is now faced with an option he has seen before, the selection of the coluan
variable. This is once again done by typing the name of the variable to be represented in the
columns ot the finished table. The student is then asked to enter the naae of the row variable.
He may enter eitner the name of the row variable or "none" indicating that a univariate table is
desired. It he has indicated a row variable he will then be asked to specify the independent
variable. After this table has been printed, the student is allowed either to select a fresh
sample, to filter further, or to obtain another table from the saae saaple.

The program contains a special error checking routine which scans every student response
for possible errors. when an error is detected the aessage "Your response was unrecognizable.
Please try again." is printed, and the prograa is made ready to accept a new response.

VOTKR in Context

The prograa has been used in two different course settings. In both the fall of 1970 and
1971 the program was used in a ju ni or- sen ior level course entitled "American Political Process"
in the University of Michigan political Science Department. In addition, in fall 1971 it was
used in another j unior- sen ior course, "Public Opinion and Pressure Groups." Less than J8X of
tne students enrolled in these classes reported any previous experience with a computer.

The first course is a large survey course in which the students are almost evenly divided
between political science majors and non-majors. while the non-majors are frequently fro* one
of the other social sciences, the course does fulfill the college distribution requireient for
the social sciences, and therefore attracts students from many areas. Due to the large
enrollment (100-150 students) this course is typically taught using a lecture format. The
content of the course concentrates on mass actors (as opposed to elites) in the political
system. Some of the major topics studied are voting behavior, public opinion, and political
pa r t ies.

In contrast the course "Public Opinion and Pressure Groups" is composed of mainly political
science majors (83%). Its focus is upon the measurement of public opinion, formation of
opinions, political socialization, models of opinion change, demographic bases of opinion, and
psychological models of opiniou change. This course is normally smaller than the political
process course (20-50 students) and is typically characterized by discussions and more student
input.

decause ot the differing foci of the two courses, the computer program was used differently
in each course. in the course on the political process which focuses on voting behavior, the
students were assigned data based term papers. The VOTER program was used to analyze one of the
current election studies of the Center for Political Studies (C.P.S.) (1). These analyses formed
the principal components of the term papers. The students were relatively free to select a
topic within the range of material covered by the base study. During fall 1971 students were
using data sets composed of 100 variables from the CPS 1970 Election Study.

3y using the cross tabulation features of the program (bivariate frequency table) students
were able to investigate the relationships between several pairs of variables, while the filter
option allowed students to control additional variables. The combination of these two features
enabled students to conduct a wide variety of analyses at a relatively sophisticated level.

The public opinion course constructed a data set based upon interviews of Ann Arbor voters
collected by the students themselves. In this way the students were able to experience first-
hand survey research through drawing a sample, conducting interviews, codiug the questionnaires,
and analyzing the results by means of this program. As in the political process class, the
students were arked to write term papers based on their analyses of the data. In addition^ to

set froi

the final interview results, the public opinion students were asked to analyze a data
the pretest of their survey instrument.

1 Because ot
students on the
students in the
their data that
analyses that
nuch easier for
na jors.

their greater involvement in the data gathering and data analysis phase, the
public opinion course were even more enthusiastic about the program than the
political process course. Some students became so interested in the analysis ot
they reguested additional assistance from the instructor to conduct some
were too sophisticated for the VOTER program. This additional involvement was
this class because it was a smaller class composed mainly of political science

In both classes initial instruction in
Terminal System (.ITS) were provided by the Depar
Proqraa. Throughout the semester both the inst
Assistance Program provided counseling in both t
provide the students with assistance when
available Monday through Priday, 9 a. m. to 5 p.
students seemed apprehensive. Informal stud
quite good, however, after an initial success at

the use of the computer program and the Michigan
tment of Political Science Computer Assistance
ructor and the graduate students in the Computer
he program aad MTS. This was designed to
they needed it. The computer assistants were
m. Before actually using the machine many
ent reactions to the use of the computer seemed
the terminal.

stud
that
of t
(1)

In order to gauge the value of the computer experience a survey was conducted ot the
ents in the two courses offered in the 1971 fall term. The results of that survey confirmed
the use of the program had been quite successful. When asked of their general evaluation
he computer experience, 56* rated it **very favorable", on a four-point scale running from
"very favorable" to (4) "very unf a vora ble." The mean score was 1.45.

The ratings of the program and the general experience did not vary between classes and did
not vary between those who had had some previous experience with the computer and those who did
not. There was no variation between political science majors and non-majors. All groups
preferred the data-based term paper to the more traditional library term paper by a substantial
margin. (85* preferred the data paper.) The students felt the data paper was easier, more
enjoyable, and more valuable. 62* thought the data paper easier, 90* thought it more enjoyable
and 88* thought it more valuable.

The general evaluati
When asked to rate how diff
(1) "very hard" to (4)
computer experience was als

on of the computer pr
icult it was to learn
"very easy", the
o quite high, 1.10.

ogra

mean

m and its documentation was also
use the program on a tour-point
score was 3.17. The mean tor t

quite high,
scale from
hose with no

One

com pu ter
computer

of the surprising findings of the survey was that 68* wanted to find out more about the
itself. Even a substantial percentage of those who had previous experience with the
(58*) were not yet satisfied and wanted to learn more.

Limitations

One of the most significant limitations on the program is that
maximum of five code categories. The reason for this is that the width of
limited to 70 characters in order to fit on the Model ii Teletype
University of Michigan. In an environment capable of handling longer line
could be easily avoided.

a variable
the output
in general
lengths, th

may have a
must be
use at the
is problem

Some student frustration was generated by the inability of the VOTER
keywords and variable names entered with minor misspellings. Although jos
suffer similar student criticisms, recent software developments could be u
minor typographical errors and misspellings. Routines which allow for
currently being developed tor future use in VOTER.

program to recognize
t current programs
tilized to allow tor
these errors are

Other Uses ot the VOTER Program

The VOTER program should be used in a course where analyzing reil data makes sense and
where the teacher’s objectives include increasing student competency in analyzing and
interpreting data. Courses in the social sciences are obvious places to use VOTES; educational
research courses, sociology, educational technology, research and design courses, political
science, survey research courses and possibly even courses in applications programming are also
suitable.

An important aspect of VOTES is that it was designed as a tool to improve instruction and
not as a substitute for the textbook or the teacher. Therefore, it can be used in a variety ot
courses and is not subject matter dependent nor is it dependent on a particular textbook, or a
particular view of teaching. It is an adjunct use ot the computer m teaching and as such has a
broad base of possible applications.

465

461

acknowledgements

The VOTEH
and Teaching at
supported in par

prograa was writ
the University of
t by a grant from

ten by Hr. Mark Ba
Michigan (currentl
the Air Force Offi

rnett of
y at Bal
ce of Sc

We would like to
VOTER evaluation surveys

thank Herbert Weisburg and Ronald
in their classes.

the Center for Research on Learning
1 State University). This work was
ientific Research (A P0SR-6B- 1601) .

Inglehart for allowing us to conduct

FOOTNOTE e

tical process was provided by the Inter-
Institute for Social Research ot the

University of Michigan.

Some of

the data used by the course on the poli

466

A STUDENT HANDBOOK OF EMPIRICAL EVIDENCE: THE UTILIZATION OF
C4P| DATA IN UNDERGRADUATE EDUCATION

Janes E. Hart:

The Ohio State University
Columbus, Ohio

This student handbook and data set were created in keeping with one of the five principal
■ issions of the Project for tha Comparative Analysis of Policy Environnents (CAPE) , under the
supervision of Professor Philip fl. Burgess, Director of the Ohio State University*s Behavioral
Sciences Laboratory:

•••the utilization of the research environment in undergraduate teaching by creating
an accessible data-rich setting with appropriate tutorial assistance to facilitate
the enpirical work of the undergraduate student***

It is expected that this student handbook will be utilized in conjunction with an
international relations laboratory manual for undergraduates, Theory, Daja, and Ana^ys^s:

t° yuantj.tqtj.ve International Poijtjcs (Burgess and Peterson, Aliyn and Bacon,

1972)7

The Burgess-Petersoo manual introduces the student to a variety of ideas and concepts about
how international data can be generated and analyzed in order to help answer some of the basic
questions confronting scholars of international politics. Specific topics include basic

considerations in the philosophy of science, principal da ta-genera ting techniques, elementary
dat a- analysis techniques, fundamental considerations of research design, and instruction in the
operation of an IBM Key Punch and Counter-sorter.

The student manual attempts furt.’—r to advance a major goal of both the CAPE Project and
the international politics faculty in the Department of Political Science: to develop a strong
interface between faculty programmatic research endeavors and graduate/undergraduate education
and training* Host of the international politics faculty have been engaged in the comparative
study of foreign policy. Specifically, research has focused upon three principal themes:

1« The exploration of the theoretical and empirical utility of a typological strategy

for understanding and organizing knowledge about nation-states.

2. The empirical utility and theoretical extension of one particular typological
framework, Rosenaufs pre-theory of foreign policy.

3. The development of satisfactory conceptions and empirically useful measurements of
foreign policy outputs.

Consequently, a student data set has been created from a larger data file, the CAPE Project
data base, which consists of a data matrix that reads 116 x 150. The 116 nations comprising the
sample size are those national political units that were members of the United Nations in 1963
or that were excluded fro# U. N. membership because of their divided status. The approximately
150 variables in the data set represent principally aggregate social accounting indicators and
external behavior attributes from the time-span of the 1960*s.

From this ever-expanding list of CAPE variables, 12 have been included in the student
handbook* This particular sot of variables was selected because each appeared to tap
specifically one of the Rosrnau variable clusters in his pr e- theoret ical ft&mevoik of foreign
policy. The list was limited to 72, each expressed in one-column fields, in order that the data
set would contain only one IBfl card per country.

The number of variables for each variable cluster is given below.

C^J.us te£ Nage

Number of V arables

Size 4
Development 4
Political Accountability 3
Governmental 7
Societal 7
External ID
Political Outputs 17

467

463

Economic Outputs

Military Outputs

WEIS Outputs

Total

The
given in

complete list
the manual.

of variables.

their ..ief init ions and

sources.

and the

coding scheme are

Sight of the 72 variables were originally in ordinal fori. The regaining 64 were expressed
at the iuterval level of measur&ment initially, but were transformed to the ordinal le/el by the
following procedure. All interval variables were normalized by appropriate data transformation
techniques, then standardized so that their mean equaled 100 and a standard deviation equaled
10, The range was compared for each standardized variable, then divided into 10 equal intervals
(deciles), ordinal value (from 0 to 9) were assigned to each decile. The values for each country
on every variable were place) in the appropriate decile, and the decile number was assigned as
tha ordinal code for each datum.

Once the student becomes familiar with the data set, he can perform any type of data-
analysis requiring either nominal or ordinal level of measurement. The Burgess-Peterson
laboratory manual suggests a variety of nominal and ordinal associat ional statistics.
Additionally, it can be argued that because the assumptions required for in te rval- level tests,
such as regression analysis, have been met by the techniques employed to convert these data to
ordinal measures, data analysis techniques normally associated with interval data may also be
performed.

The variables in this data set have been assigned to columns 1-72. Columns 73 and 77 are
blank. Three-letter and three-digit IRA codes for each country are given in columns 74-76 and
78-80 respectively.

The data set punched on IBM cards may be obtained from the Behavioral Sciences Laboratory.

£ar t I: Introduction to the Student

This handbook is designed to help the undergraduate student engage in his own research
endeavor in order to uncover information about the how9s and why's of a nation's behavior in the
international arena. It is assumed that this manual will be utilized in conjunction with a
companion volume: Jheo£x, £ata, Afiilysis: An Introduction to Quantitative International
Poetics, (Philip n. Burges3 and Lawrence E. Peterson, Allyn and Bacon, 1972). Whereas, the
Burgess-Peterson manual describes ho* one executes a research design (theory-building, data-
generating, and data-analy sis techniques, etc.) , this handbook describes a specific framework
for understanding foreign policy behavior, and generates and explains the use of a data set
created from a larger data file in the Ohio State University's Behavioral Sciences Laboratory
specifically for undergraduates. By using both this and the Burgess-Peterson manual, you should
develop some preliminary skills for doing your own research, as well as appreciate the many
problems associated with such endeavors.

Par£ II: Nation a^d Variable Classification Schemes

If we are going to search out the influencers of nation behavior, or at least ascerta?u
which set of conditions is present when a certain behavior pattern occurs, we need a framework
which will allow us to distinguish among various types of nations. In this fashion we can
investigate the influencers of behavior for a selected subset of nations as well as for the
entire universe of nations-

This framework should also allow us to make some initial judgments about which kinds of
influencers are important. That is, the framework should identify variables or clusters of
variables which ought to be utilized in any analysis of foreign policy behavior.

One researcher at Ohio
classified or typed according
variables)'1: (1) the size of a

and underdeveloped) ; and (3) pa
thres national attributes ars
given in Figure 1.

State, Professor Rosenau, has suggested that nations
to three dichotomized attributes (what he terms
nation (large and small); (2) its level of development
litical accountability (open and closed societies),
combined, eight types ("genotypes'1) of nations emerge

ought to be
"genotypic
(developed
If these
• These are

£64

cue

Small

Deve loped

Underdeveloped

Developed

Underdeveloped

Open 1 Closed

0p*i | Closed

Open 1 Cloaed

Open 1 Closed

FIGURE 1 . Nation Genotypes

A variable strategy which you lay wish to adopt in your research is to use as your sample
size oaly chose countries falling into one category of nations. For example, you may wir.h to
utilize only one attribute such as size in order to examine the behavior of nations within
either the large or the small jroup. Alternatively, you nay use all threo genotypes to create a
subset of nations, such as the large-developed-closed group of nations, for the purpose of
analyzing behavior. Conseguently, Figure 2 reveals the genotypic category for each nation in the
year 1963. The specific leas uras ^utilized for each genotype are given below:

size - total population

development - GNP/capita

political accountability - freedom of the press

The data set generated for this class contains several measures for each oi these three
variables, which will allow you to create a typology of nations by utilizing other indicators of
he genotype. Alternatively, you may wish to use the measures of size-development-political
accountability in the actual proposition which you are testing. For example, the proposition -
As the size of a nation increases, the amount of hostile activity in which it engages will also
increase - uses the size variable in a way other than for typing nations. The Rosenau franewori
also suggests that behavior is influenced by individual, governmental, societal, external, and
systematic attributes. Conseguan t ly, data representing some of these clusters (individual and
systemic influencers are eliminated because of a dearth of data for the time span of this
handbook) are included in your data set of 72 variables. Thirty-five of these may be considered
input or independent variables; that is, they represent attributes of nations - their size.

level of development, degree of political accountability, governmental and societal factors, and
external variables (geographic position vis-a-vis the major powers, national attributes in
comparison to one*s neighbors, and access to the seas). This list of variables follows:

UrM tail

Developed

Underdeveloped

Developed

Uederdaveloped

Open J

( Cloaad

Open j

| Cloeed

Open |

| Cloeed

Open

Cloeed

tan ea - 229
W. Car macf - 295
Italy - 929
Japan - 740
O.K. - 200
0.9. - 002

Poland - 290
0. 1.9.1. - 945

ft null - 140
India - 790
8. Korea - 792
Mexico - 070
■lferla - 479
PMUppUee - 940
lhailaad - 900
Turkey - 440

Red China - 710
Iudoneele - 890
Pakletan - 770
9 pain - 230
U.A.R. - 491

Argentina • 180
Auetrelle • 900
Auetrle - 305
ftelglua • 211
Canada - 020
Cypr-a - 352
Dtnrark - 390
Finland - 375
Ireland - 205
Ierael - 666
Wither land* - 210
lew Zealand - 920
Koruny - 985
Widen - 380
•vie car Land - 225
Veoeauala * 101

Iceland - 395**
Kuwait - 690
Luxembourg -
Trinidad and
Tobago - 052

Albania - 359
Bulgaria - 355
Czechoe lovakla
- 315

K. Gemeny - 265
Hungary ~ 310
Rueanla - 560

Bolivia - 145
China (T.) - 713
Colombia - 100
Coeta Rica - 094
Doe. Rep. • 042
Ecuador - 130
El Salvador - 092
Grreca - 350
Gua .Mala - 090
Hrv*duraa • 091
J arnica - 051
Lebanon * 660
Malaya la • 820
Morocco - 600
Panama - 095
Faru - 135
S. Africa • 560
Uganda - 500
Uruguay - 169

Burundi - 516
Cantral African
Ra public - 482
ChlU - 155
Congo (Br.) - 484
Dahomey - 434
Gabon - 481
Guinea * 438
Ivory Coeet - 437
Llbarle - 450
Libya - 620
Malagaay - 580
Mall - 432

a - 19

Afghani! can - 700
AlAerla - 615
Bum - 775
Cambodia - 811
Cameroun * 471
Ceylon • 780
Chad - 485
ConBo (Kl.) - 490
Cube - 040
Ethiopia - 530
Ghana - 452
Haiti - 041
Iran - 630
Iraq - 643
Jordan - 663
M. Kora# - 731
Laoa - 812
Nepal - 790
Portugal - 235
Senegal - 433
S. Vietnam - 817
Syria - 652
Tunlala - 616
Upper Volta - 439
Yugoalevle - 345

Mauritania - 435
Mongolia - 712
Hlcaregua - 095
Niger ■ 456
N. Vietnam - 816
Paraguay - 130
Rwanda - 517
Saul! A'.ebla - 670
Sierra Leona - 451
Somalia - 520
Sudan - 623
Togo - 461
Taman - 678

I * 25

* Cut-off polet - mean

Mean of pop. • 26.757

Mean of Dev. • 527.9310

Heee of open-cloeed - 458.3678

** Hleelng gate for the political
accountability variable

1-6

a - 2

a - 8

a- 3

a • 16

FIGURE 2. 1963 Genotypic Nation Clusters by Means*

469

465

£ar t II J: Varia bje Definitions ^nd Sources

The wita set outlined in Part IX has been extracted from a larger data base developed under
the CAPE (Comparative Analysis of Policy Environments) Project. This latter project has been
conducted by the Behavioral Sciences Laboratory at the Ohio State University. The CAPE Project
data base consists of a data matrix with row and colunn dimensions of 116 x N. The number 116
represents those national political units that were members of the United Nations in 1967
that were excluded from membership because of their divided status (such as North and liCith
Vietnam). The number N represents the number of variables in the data set at a given moment, a
list which is constantly expanding as user needs continue to change.

The student data set utilized in this handbook contains 72 variables. Thus the data matrix
is 116 x 72.

The data set has been placed on IBM punched cards which each student will receive. A
standard punched ca rd . cont ai ns 00 columns, in each of which can be pJaced one unit of
information. Information or data are arranged in fields; thus, if each datum can be placed in
one field, a maximum of 80 units of data may be placed on one card. Since the data set is
composed of 72 variables, it is possible to place all of the information for each nation on one
card. The complete data set has been punched on 116 cards, each of which represents one nation
of our sample.

The one-field code values assigned to the 72 variables are given in the first 72 columns.
Three-letter and three-digit codes for each country are given in columns 74-76 and 70-80
respectively. Por example, the card representing the data for the United States contains the
letters "USA" in columns 74-76 and the numbers rt002M in columns 70-80.

The country identifications and definitions of variables 1-10 are given below.

(Definitions of variables 11-72 should be obtained from the author.)

002 USA United States

020 CAN Canada

040 CUB Cuba

041 HA I Haiti

042 DCM Demin lean Republic

051 JAM Jamaica

052 TRI Trinidad and Tobago

070 HEX Mexico

090 CUA Guatemala

091 PON Honduras

092 ELS El Salvador

093 NIC Nicaragua

094 COS Costa Rica

093 FAN Panama

100 COL Colombia

101 VEH Vena sue la

130 ECU Ecuador

133 PER Paru

140 BRA Brasil

143 BOL Bolivia

130 PAR Paraguay

133 CHL Chi la

160 ARC Argentina

163 URU Uruguay

200 UMC United Kingdom

203 IRE Ireland

210 NTH Netherlands

211 BEL Belgium

212 LUX lux*abourg

220 PRM Fra >ca

223 SVZ Jt/lt garland

230 SPN Sp-»ln

235 TC£ Portugal

255 OW Host Germany

265 GNI Fist Germany

230 POL Poland

305 A US Austria

? 10 HUN Hungary

113 CZE Cscchoslovakla

325 ITA Italy

339 ALB Albania

343 YUG Yugoslavia

350 GRC Greece

332 CYP Cyprue

353 BUL Bulgaria

360 RUM Rumania

363 USR USSR/Russ la

375 PIN Finland

300 SVD Sweden

383 NOR Norway

390 DEN Denmark

395 ZCt Iceland

432 K.Z Mall

433 REN Senegal

434 DAH Dahomey

435 MAU Mauritania

436 MIR Niger

437 I VO Ivory Coeat

430 GUI Guinea

439 UFP Upper Volta

450 LBR Liberia

451 SIX Sierra Leona

45.1 GBA Ghana

461 TOG Togo

474 GAO Cameroon

475 NIC Niger la

401 GAB Gabon

402 0KM Can* African tap

403 CHA Chad

404 CON Congo (Br

490 COP Congo (XI.)

500 OGA Uganda

516 BUZ Burundi

517 RVA Rwanda

520 SOM Somalia

530 ITH Ethiopia

560 SAP Soutu Africa

500 MAG Malagaay

600 M0R Morocco

615 ALU Algeria

616 TUN Tunisia

620 LBY Libya

625 SUD Sudan

630 IRN Iran

640 TUR Turkey

645 IRQ Iraq

631 OAR United Arab Republic

652 SYR Syria

660 LEB Lebanon

663 JOS. Jordan

666 ISR Israal

670 SAU Saudi Arabia

670 TEM Taman

690 KUH Kuwait

700 ATG Afghanistan

710 CHN Rad china

712 MON Mongolia

713 CHI China (Taiwan)

731 ROM North Koret

732 K0S South Korea

740 JAP Japan

750 IMD India

770 FAK Pakistan

775 BUR Burr

700 CEY Cayloa

790 NKF Nepal

000 TAX Thailand

011 CAM Cambodia

012 LAO Laos

816 VTK North Vietnam

017 VTS South Vietnam

020 HAL Malaysia

040 PHI Philippines

050 INS Indonesia

9C3 AJL Australia

920 m New Zee.' and

TABLE 2. Country Identification Ksy

iatiabls fisiiaitiM*

Va ciafeis 1: I2iil

Variable fiifiaitASQ: "The total population of a country is coov eutionally descrit*»d

as £g gactg or £e 35lS* A true da f $cto or present-in-area concept iaplies that all
persons physically present in the country - residents and no.i-residents alike - have
been counted in the local area where they were found at the tine of the census. The
dp 1 U£e count, in contrast, comprises all persons vho usually reside in the area,
irrespective of where they night happen to be at the tin# o£ the census. Sisple as
these concepts appear, strict conformity to either of then is rarely found •••• In
an effort to provide better information for constructing world and regional
population aggregates fron the results of censuses taken around 1930, the Population
Commission of the United Nations recommended a " agji(ig<} de tabulation of the

total population in addition to ary other total used for national purposes. This saae
concept was included in the EtiBSifilSS A3& Hegoa lends tjoas National EjOPUlAtlon

Censuses designed to provide guidance for the taking of Nation! Population Cyns^ses
designed to provide guidance for the taking of the 1960 cycle of censuses* In the
1960 reconnendations, the new total was called "in ter national conventional total*,
and it was defined is "the total nuaber of persons ; i esent in the country at the tire
of the census, excluding foreign ailitary, naval and diploaatic personnel and their
families located in the country but including nl itary, aaval and diploaatic
personnel of the country and their families located abrord, and aerchant seaaen
resident in the country but at sea at the tiae of the census*#** Since the coaputed
total was called for in addition to any other total used for national purposes, there
is no expectation that it would necessarily have been used in the detailed census
tabulations. Therefore, beginning with the 1 £*&£&£££» the assumption

that all census results refer to the modified i£ facto population was abandoned, and
the aodification has been described only where it is known to have been made."
"Unless otherwise noted, population figures are present-in-a rea estimates for the
present territory."

The data is in thousands of persons. The year of the data is 1963.

Citation: Demographic Yearbook 1966, 135th Issue, Statistical Office of the United

Nations, Department of Economic and Social Affairs, New York, 1967.

Vfltfrab^e Pet jnjtjQg- "Unless otherwise specified, all of these figures are assuaed to
represent~total area, that is, they comprise the land area and inland waters,
excluding only polar regions and some uninhabited islands* Inland waters are 'ssumed
to consist of major rivers and lakes .... in this yearbook, a yea is given ^ square
S.il2E®ters, the conversion fron sguare niles (if required) having been accomplished
by equating 1 sguara nile to 2.589996 square Kilometers. M

citation : Demographic Yearbook 1963, Statistical Office of the United Nations,
Department of Economic and Social affairs. New York, 1964.

Va£i§£^e Definition: GRP in millions of U. S. dollars* No definition given in source.
For a definition of GNP refer to Sprecher GNP (Cape Variable 053).

The iata is for the year 1963.

Citation: "Estimates of GNP, 1963," Agency for international Development, Report

ControI”*137, (01), Statistics and Reports Division, February 19, 1965.

Vf yl§ble pefijft jt jon: KWH of electrical production for 1963. "...All the figures on

capacity and production represent combined totals for electrical utilities and
industrial ^establishments having generating facilities for for providing all or part
of their own requirements." s

The data is in millions of KWH.

Citation : world Power Data, 1964, Bureau of Power, Federal Power Commission,

Washington, flay 1966.

Vatiabie £: Tofcal tafid &£§a

JLiEiasis i: latal sup

Xatiable 45 KjJH of £le£tfi£al C£2da£ti2a

471

latiabia $'• gmp Pe^ £a£ita

Variable Bfeiiflitjgft: GMP pec Capita. No definition given in source. T ae data is in
(J. S. dollars pec capita. The year of data is 1963.

Citation: Statistics and Reports Division, Agency for International DevelopmeM,

Pebruary 19, 1965.

Vitiate finatax ceasni^iiaa tat £a£ita

Va£iabje fiel ifiit ion : A *ationas total energy consaaption divided by its total
population. All data are iior 1963. The unit of leasure is aetric tons of coal
equivalents per capita.

Citation: Total Energy Consumption: World Energy Supplies 1962-1965, Departaent of

Economic and Social Affairs, Statistical Office of the United Nations, New Tori,
1967.

Variable 7: i£ uitgrai Workers £ of Jotai Economically &£tiye fcogul^tigg

Va£ j-nitjon; "Agricultural population for the purpose of this table nay be
defined as all perrons actively engaged in agriculture, forestry, hunting and fishing
for a livelihood, that is to say, persons actively engaged in agriculture, forestry,
hunting and fishing and their non-working dependents.... In general, the economically
active population is defined as all persons engaged in an economic activity, whether
eaployers, own-account workers, salaried employees, or unpaid workers assisting in
the operation of a family farm or business. Similarly the population economically
active in agriculture includes all economically active persons engaged principally in
agriculture, forestry, hunting and fishing.**. This general definition differs
somewhat from country to country, in some countries, for example, the estimates are
based on data relating to all persons reporting an occupation, whether or not they
were actually working at the time of the census or survey; in others, on data
regarding persons actually employed during a specific short period, unemployed
persons seeking work being excluded. Some countries report information on economic
activity for persons of all ages, others only for persons of specified ages, e.g., 14
years of age and over."

The data are expressed as a percentage and are for the year 1965.

Citation: Production Yearbook 1966, Vol. 20, Pood and Agriculture Organizations of

the United Nations, Rome, 1967.

Variable 8: £WH £er Capita

Variable kwh per capita for 1963. The data were calculated within the

source. "...All the figures on capacity and production represent combined totals for
electrical utilities and industrial establishments having generating facilities for
providing all or part of their own eguirements. "

dilation: World Pjwer Data, 1964, Bureau of Power, Federal Power Commission,

Washington, flay 1966.

Variable 9: Current gjectg^aj System

Variable Qe £ in it ion: A = Competitive (no party baa, or ban on extremist extra-
constitutional parties only) ; B = partially competitive (one party with 85>* more

of legislative seats) ; C = non-competitive (single-list voting or no elected
opposition) •

Citation: a Cross-Polity Survey, Arthur S. Banks and Robert B. Textor, The H.I.T.

Press, Massachusetts Institute of Technology, Cambridge, Massachusetts.

v aria ole 22 • Freedom of the Press

Variable fiefinitign: Freedom of the press scores - 100 (PICA index ♦4). The PICA
index is based on 23 indices of freedom of the press. The strength of the indices
were judged by both native and non-native judges in response to a questionnaire. The

468

472

scores were averaged separately for the native and non-native judges. there there
were disagreements of sore than 6 per cent between the averages, only the non-native
averages were used. Where there was less than a 6 per cent disagreement, the average
of the two was used for the PICA index.

Citation : PICA: Pleasuring World Press Preedom, Lowenstein, Freedom of Information
Center, University of Hissouri, 1966.

IV; Viable Coding Scheme

In this section the coding scheme and specific categories for each variable will be
revealed, all of the variables in the data set distributed to you are in ordinal measures. That
is, each variable has been divided into categories and assigned a number in such a fashion that
each number stands in a definite relationship to every other number; itvs quantity is greater
than or less than that represented by the remaining numbers. For example, variable 15 represents
the current status of the legislature1 s effectiveness. This variable is divided into 4
categories, numbered in the following fashion:

1 = fully effective

2 = partially effective
J = largely ineffective
4 = wholly ineffective

v'<

As you can observe from the category names, it is impossible to ascertain the exact
distance between each category (as you could with a variable which revealed the number of times
the legislature overrules the executive's veto, for example). You only know that if a nation has
been assigned the code value ,,2M, the effectiveness of its legislature is greater than that of a
nation which has been assigned the value H3", but less than that nation whiph is given the value

«t j it

In their original format, some of the 72 variables selected for the data set were ordinal
in nature (8) while most were comprised of interval-level data (64). All interval-level measures
have been reduced to ordinal data for the purposes of this manual. This was done for two
reasons. First, since a student will not become familiar with statistical techniques requiring
interval data (such as regression analysis) until later in the course, ordinal measures will
suffice for the earlier portion of the course.

The secoud reason is convenience. In order to keep the number of cards in the student's
data deck to a small number (one card per country) it is necessary to fit 72 variables on one
card allocating one column par variable. Since interval measures n require more than one columm
to express uhe value of the datum, ordinal measures are chosen instead.

Bata The following steps were employed to reduce the data to the ordinal

level of measureaen t:

a. The interval- le vel variables to be included in the analysis deck were "pulled out" of

the larger CAPE data files and standardized with a mean 2 100 and a standard

deviation - 10. The distributions for each variable had already been normalized
(aean=median=mode) with appropriate data transformations. (These terms are explained
in the Bur gess- Peter son laboratory manual and will be discussed fully in class).

b. The range of the standardized data was computed for each variable.

c. Each range was divided into ten equal interv (deciles).

d. ordinal values from 0 to 9 were assigned each decile with 0 denoting the lowest
decile and 9 denoting the highest.

e. The values for each country on every variable were placed in the appropriate decile.

f. The decile number was assigned as the ordinal code for each datum.

The ordinal values for variables 1-10 are given below. Values for variables 11-72 can be
obtained from the author.

473

4(19

C£<linal Values tor Variables

VARIABLE Is TOTAL POPULATION

VARIABLE 4: KWH OF ELECTRICAL PRODUCTION

0 - 74.87 to 80.47

1 - 80.48 to 86.08

2 - 86.09 to 91.69

3 - 91.70 to 97.30

4 - 97.31 to 102.91

5 - 102.92 to 108.52

6 » 108.53 to 114.13

7 - 114.14 to 119.74

8 • 119.75 to 125.35

9 - 125.36 to 130.96

0 - 81.10 to 85.48

1 - 85.49 to 89.87

2 - 89.88 to 94.26

3 » 94.27 to 98.65

4 - 98.66 to 103.04

5 - 103.05 to 107.43

6 - 107.44 to 111.82

7 - 111.83 to 116.21

8 - 116.22 to 120.60

9 - 120.61 to 124.99

VARIABLE 2: TOTAL LAND AREA

VARIABLE 5: GNP PER CAPITA

0 - 72.27 to 77.70

1 * 77.71 to 83.14

2 • 83.15 to 88.58

3 - 88.59 to 94.02

4 " 94.03 to 99.46

5 ■ 99.47 to 104.90

6 - lo4 . 91 to 110.34

7 - 110.35 to 115.78

8 - 115.79 to 121 22

9 - 121.23 to 126.66

0 - 81.38 to 85.28

1 - 85.29 to 89.19

2 = 89.20 to 93.10

3 « 93.11 to 97.01

4 » 97.02 to 100.92

5 - 100.93 to 104.83

6 - 104.84 to 108.74

7 • 108.75 to 112.65

8 • 112.65 to 116.56

9 - 116.57 to 120.47

VARIABLE 3: TOTAL CNP

VARIABLE 6: ENERGY CONSUMPTION PER CAPITA

0 » 83.10 to 87.84

1 " 87.85 to 92.59

2 - 92.60 to 97.34

3 - 97.35 to 102.09

4 - 102.10 to 106.84

5 - 106.85 to 111.59

6 - 111.60 to 116.34

7 - 116.3: to 121.09

8 » 121.10 to 125.84

9 - 125.85 to 130.58

0 • 77.90 to 82.10

1 -82.11 to 86.31

2 - 86.32 to 90.52

3 - 90.53 to 94.73

4 - 94.74 to 98.94

5 - 98.95 to 103.15

6 - 103.16 to 107.36

7 - 107.37 to 111.57

8 - 111.58 to 115.78

9 - 115.79 to 119.99

470

474

VARIABLE 7s ACRI CULTURE WORKERS AS 7. OF TOTAL ECONOMICALLY ACTIVE POPULATION

0 - 81.20 to 85.36

1 - 85.37 to 89.53

2 - 89.54 to 93.70

3 - 93.71 to 97.87

4 - 97.88 to 102.04

5 - 102.05 to 106.21

6 - 106.22 to 110.38

7 - 110.39 to 114.55

8 - 114.56 to 118.72

9 - 118. 73 to 122.89

VARIABLE 8: KWH PER CAPITA

0 • 74.78 to 79.30

1 • 79.31 to 83.83

2 • 83.84 to 88.36

3 • 88.37 to 92.89

4 • 92.90 to 97.42

5 • 97.43 to 101.95

6 - 101.96 to 106.48

7 • 106.49 to 111.01

8 - 111.02 to 115.54

9 • 115.55 to 120.07

VARIABLE 9: CURRENT ELECTORAL SYSTEM

1 • Competlteve (no party ban, or ban on extremist or extra-constltutlona 1
parties only).

7 m Partially c jpetltlve (one party with 851 or more of legislative
seats).

3 m Non-competitive (single-list voting or no elected opposition).

VARIABLE 10: FREEDOM OF THE PRESS

0 - 82.90 to 86.58

1 * 86.59 to 90.27

2 - 90.28 to 93.96

3 - 93.97 to 97.65

4 - 97.66 to 101.34

5 - 101.35 to 105.03

6 ■ 105.04 to 108.72

7 - 108.73 to 112.41

8 - 112.42 to 116.10

9 - 116.11 to 119.79

; J

475

THE CBEAIIOI AID DIFFUSION OP IIIOVAtIVB OSES OP THE
COflPOTEI II SOCIOLOGY EDOCATIOI

Boaald Stiff
Onitl Vanderportaele
Illiaois Iaatituta of Technology
Chicago, Illinois 60616
Telephone: (312) 255*9600

This seeas an appropriate tiae to evaluate the creation aad diffusion of innovative uses of
the coaputer in sociology education. it is the tine to ash "to what extent have we been
innovative” and "to what extent have these innovations diffased through the educational
coaaunity"? Toward these goals we propose a classification scheae suggestiag several possible
innovative approaches. Published innovations are compared to this scheae to evaluate the extent
to which we have exhausted these innovative possibilities. To evaluate the feasible diffusion
of these innovations a briaf analysis of the potential sites for adoption of coaputer based
educational aaterials is developed. The likely actual diffusion of these coaputer enriched
educational aaterials is aatched against these potential adoption sites. In concluding several
suggestions for encouraging craation and diffusion of innovative coapater based educational
aaterials are aade.

Soae portions of this paper are based on experiences gained during the initial three years
of "A Cooperative Venture in Curriculum Oevelopaeat Based on a legional Coaputer letwork at
Illinois Institute of Technology (1) "• Bonald Stiff was Project Banager for the project which
involved coaputer based curriculua development in seven academic disciplines at ten aidwestern
colleges supported by the I.I.T. UIIVAC 1108^ Daniel Vandeportaele served as Sociology
Curriculua Development leader.

Classification of Innovations

Numerous classifications of computer uses in education have been proposed. Luehraann's
(1971) ten nodes is one of the aore useful:

”1. Hanageaent of instruction and aaterials.

2. Adainistration of drill and practice sessions.

3. Conversations and dialogs.

4. Large data-base inguiry systems.

5. simulation.

6. Problem solving.

7. Laboratory data analysis.

8. Laboratory data acquisition.

9. Control of experiments.

10. Production of graphics, aovies and other nedia."

Although Luehraann is a physicist, these nodes are all suitable for use in education in
sociology. (Laboratory, of course, has a soaewhat different meaning to sociologists than to the
physicists.) The scheae, however, can be aade more useful by consideration of the substance of
sociology.

Although methodology and theory are recognized as interdependent, for instructional
purposes it is often useful to treat each independently. Additionally, at tines we deal with
concepts, at tines with empirical data. Based on these factors we have developed the following
substantive classification for instructional uses of conputers in sociology:

Methodology

Theory

(A) Programs which

(B) Programs which aid

Conceptual

teach methodological
concepts and the logical
basis of scientific
inquiry.

in theory construction
through application of
symbolic logic and the
creation of models.

Data Specific

(D) Progm ms to develop
"causal models" or test
theory through sensi-
tivity analysis.

477

Our sociology specific schene nay ba sapariaposed on Luekrnann 1 a to produca up to forty
possible coaputer based educational strategies. Of course, several of these sake little sense
(e. g. 7A, 3B, etc.) but aost provide useful suggestions for educational innovations. For
exanple, large scale data bases nay be developed containing both data and propositional
inventories. The propositional inventories nay be used to denoastrate the concepts of theory
building (4B) . Data nay then be used to develop causal nodels testing these theories (4D) .
Anyone who has atteapted to coaaunicate the concepts of internal and external validity in
experinental design (e. g. regrnssion artifacts, history, etc.) would be likely to welcone a
conversational prograa denonstrating these nethodological concepts (31). Coaputer based dialogs
nay be developed to instruct the student in strategies of interviewing (31)- Other
possibilities are suggested by this schene but it is not our goal to be exhaustive, but to
denonstrate the suggestive potantial provided. This schene also provides a standard tor
evaluating the extent to which innovative possibilities have been explored. 3ext, however, we
consider the potential diffusion of coaputer based educational naterials in sociology.

possible Diffusion o£ Tfrese innovations

An educational innovation is sociology could originate at one or nore of the over BOD
colleges and universities offering an undergraduate najor in sociology and diffuse to sone
portion of the renainder. Since aethodology courses are the aost obvious settings to introduce
the coaputer we night expect initial innovation at schools requiring research nethods or
statistics for their najors(2). In addition to having a potential need for introducing coaputer
innovation^ the sociology faculty nust have access to a coaputer facility. Hanblen (1971)
reports that about half of the 2,500 institutions of higher education (including junior
colleges) have sone coaputer facility. Be would expect a reasonable positive correlation
between schools requiring aethodology courses of their najors and schools having a coaputer
facility. Therefore, it does not seen unreasonable to estinate that over 200 colleges have both
course requirenents and coaputer facilities pernitting perhaps even encouraging, innovations in
coaputer supported sociology education.

An argunent can be nade that coaputer facilities at nany colleges are not substantial
enough to perforn effectively the aost obvious use, statistical, analysis of large data bases.
(Strategy 3C) . The snail coaputers (e.g. IBM 1130) available at nany colleges seldoa have
sufficient processing speed or suitable statistical libraries for neaningful data aaalysis.
Although this nay be true in part, this problea is virtually eliainated at snail colleges who
aake renote use of larger coaputers at universities, in their region. Since I960 the National
Science Foundation, Office of Conputing Activities, has provided support of regional conputing
activities whereby universities with aajor coaputer hardware and software act as a resource for
several participating schools. Through 1971, 23 regional networks had been established,
assuring conputing resources for 220 colleges and universities. Assuning half these schools
offered sociology as a aajor at least 100 colleges and universities have had access to a
university coaputer center and presuaably sone rewards would be gained by naking use of this
resource.

In sunnary, we have deaonstrated that there are aunerous ways in which the coaputer nay be
used to enrich sociology education. Also# there appears to be at least 100, if not several
hundred, colleges and universities which have both coaputer resources and course requirenents
encouraging innovative use of the coaputer in undergraduate education- Relative to this
theoretical nosaic what has bean acconplished?

jjha t Has Been ^ccoap^ished

Published reports of conputing activities supporting undergraduate sociology education
suggest that students at large schools with large coaputers are analysing data bases in
aethodology courses. Returning to the original classification schene this is strategy 4C.
Pedagogical differences in data base analysis include, having students gather their own data
(O'Kane: 1970), reaching hundreds of students (Anderson and HcTavish, 1970), providing rich
data bases and inexpensive conversational analysis (Heyers, 1970 and Davis, 1971), instant
turnaround (Kreider, et. , Sim, et . al. , 1971) , and use in an underdeveloped area with a
PDP/10 coaputer (Nildgen; 1*171). In searching for uses other than data specific aethodology
using large data bases (4C) cur rewards are few.

Vargus and Unite (IS /I) have used siaulation progress in an Urban Affairs course to
denonstrate infornal neighborhood social integration (Strategy 5D) • Vandeportaele has developed
nodels of three-aan doaiaance and hunan interaction (Honan's propsitions) that are problea-
solving denonstrations of tho concepts of theories (Strategy 6B) and a Coaputer siaulation of
the growth of urban areas (Strategy 5D) • Nicholas flullins, Indiana University, has developed
conversational prograas denoist rating concepts in theory construction (Strategy 3B) and causal
aodeling (Strategy 3D).

The najority of the reported innovations applying coaputers to undergraduate sociology
education have considered varieties of data base analysis in aethodology courses, of the up to

39 other possible strategies a great deal of creative potential remains. The sources of these
innovatioas reveal additional opportunities for creation and diffaaion of innovations.

It is instructive to consider the sources of the papern accepted at the first two
conferences on coaputers in undergraduate education. Sociology papers were written by aathors
at ten schools with a aedian . t udent population of 10,000. lone of these schools were reaote
participants in the M.S.F. funded regional coaputer network!, although three provided the
network central coaputing resources. Although there are nunerous schools with under 2,000
students only one paper origimted froa a school of this si7e. lith the exception pf, Francis,
flcGinnis, and Schnell9s (1970) discussion of the future desirability of reaching nnall colleges
none of the papers considered the diffusion of coapater innovations to other schools.

There is a strong suggestion, although neither proof nor explanation , that aodest sice
colleges are aaking virtually no use of the coaputer in undergraduate sociology education. Our
experiences at Illinois Institute of Technology as an M.S.F. funded regional coaputer activity
provide partial explanations for poor diffusion of the coaputer innovations to snail colleges.

During the initial three years of the project an average of one sociologist per caapoa
participated in the sociology curriculua development project (3). Each participating faculty
aeaber averaged about 20 ainutes of coaputer tine annually, while assisting 20 students. During
this period we provided about 50 coaputer prograas for data base analysis (Strategy 7C) and
several other strategies. The3e prograas were adequately designed and docuneated, but certainly
not as highly polished as aost text aaterials and teacher1* aanuals(4). Virtually none were
adopted by our participating faculty with the exception of soae ainor statistical routines (5) •
At no tine did we achieve any significant ase of these prograas. Therefore, this year we have
turned totally to the use of statistics prograas to analyze data bases (Strategy 4C) . Ve are
not aware of any other substantial adoptions of coaputers by sociology faculty at snail schools.
There are certainly nore than we list here.

He attribute this lack of success to several conditions, external and internal to these
schools. External to the college is the general failure of sociologists to create coaputer
applications which are suitable for use in undergraduate education. "Coaputer assisted"
sociology, beyond data analysis, does not seen to be one of the stronger forces in sociology
today. Secondly, very few PhD graduates in sociology are trained in coaputer usage other than
data analysis. Thirdly, with the exception of Dartaouth's project IHPBESS (a systen which is
quite difficult to export due to its prograaaing specifically for Dartaouth9s coaputers ), there
has been very little research funding for developaent of coaputer enriched sociology teaching
aaterials and systeas.

Hithin the college there are additional probleas. College administrations are seldoa
aggressively encouraging faculty developaent. Faculty at naay schools have heavy teaching loads
and low salaries, often leading to a need for suppleaentation through suaaer teaching. Little
tine is available for developaent and utilization of new skills. This contributes to rather
fixed and frequently out-dated curriculua in which adoption of the coaputer has a very low
priority. This aay result froa other aaterial having an absolutely higher priority or the
coaputer providing absolutely too auch pain. Additionally, there is always the fear of
alienating students by exhibiting personal liaitations or teaching "noa-huaanistic" sociology.

In suaaary, of all possible innovative strategies for using coaputers in sociology
education few have been exploited. Of all possible sources for creating innovations and sites
for diffusion few have responded. Evaluated in teras of opportunity ve can be optinistic about
the possibilities that reaain open. But how can ve take advantage of the current "crisis" in
coaputer enriched sociology education?

In Conclusion - How Can Hg IflC2UL&g® Innovation and Diffusion

He have made an arguaent for two needs or opportunities in the creation of coaputer
innovations and the diffusion of these innovations. The initial creation of several innovations
shou; d not be difficult. The scheae for categorizing educational uses of the coaputer presented
in ti.is paper suggests several new directions. Soae teaching aaterials aay be developed without
external research funding, although funds directed into the undeveloped uses and aultiple
researcher and school cooperative ventures are likely to produce a substantial aarginal return.
Funding agencies should provide incentives for directing efforts toward developing innovative
naterials in the numerous underdeveloped strategies (6) .

A greater barrier to widespread coaputer usage in sociology education is the problem of
diffusing existing innovations. The only prograas achieving reasonable wide spread distribution
are data analysis systeas(7). Statistical package for the Social Sciences (S.F.S.S.) is the
best docuaented and lost widely diffused of these programs. He have found teaching sub~sets of
5.P.S.S. quite satisfactory for use with seniors and graduate students. When allowing optional
use in a aethodology class, ten of 34 students elected to use S.P.S.S. at a cost of SS50. This
cost is excessive for a single course and can only be marginally justified if it is the

479

474

studont's only exposure to coapator analysis or it is cost; ' over the total class sise at Ilk
per student. These systeas are jften veil docuaented and provide sufficient flexibility for an
instructor to adapt then to his own knowledge and style of teaching. In this nanner analysis
systems close the gap betvaen innovation and diffusion by reducing the need of the sociology
faculty to becoae coaputer knowledgeable, to develop texts, or to reprograa.

This suggests opportunitias for speeding diffusion of coaputer innovations; the developaent
of veil docuaented, pedagogically flexible progranning systens, requiring virtually no coapo :er
knowledge by the consuaer, inexpensive to use, and transportable over a vide variety of coaputer
systaas. Thus a theory building coaputer enriched teaching unit should pernit a variety of
aethodological and theoretical peLspectives. original creation of transportable prograaaing
systeas of this sort will be guite costly. The gr^l of such projects, however, is vide spread
diffusion and the cost per adopting school and stadeat reached could be guite low. Ve do not
believe these systeas can he developed without funding agencies encouraging tean efforts and
high standards for the initial developaent.

it the sane tiae thesa progran systeas are being developed sociology faculty should be
trained in the use of the coaputer in education. In our regional network ve have deaoastrated
that this training is not effective on a part-tine basis. Pull tiae, four to eight week suaaer
institutes aodeled on those sponsored by the Rational Science Foundation seen the aost effective
strategy (6), Suaaer institutes can produce coaputer capable sociologists at a cost of about
13,000 per sociologist. If ve assune that £ faculty nenber is able to effectively coaauaicate
his skills to 200 students in a five year period following conpletioa of the suaaer institate an
expenditure of SIS per student results. Two institutes could produce 50 to 80 coaputer
coapetent faculty aeabers annually. The suaaer institute setting eliainates soae of the
institutional constraints on faculty developaent and provides an excellent opportunity for
faculty at a variety of schools to exchange knowledge over several weeks. It aay be desirable
to select participants on a regional basis to encourage connunication following the institute.
If two or aore institutes are held in a given year, instructional resources should be shared to
provide a variety of viewpoints.

In conclusion, ve beliave that those of us who support this annual conference should
restructure conference sessions to encourage innovation and diffusion of the coaputer in
sociology education. One session should be devoted to innovative coaputer enriched teaching
aaterials. Developaent of uses other than analysis of data bases should be encouraged. 1
second session should be devoted to the diffusion of coaputer enriched teaching aaterials.
Experiences at schools of various sixes and character should be r*ncouraged. Instances of
aaterials being adopted at one or aore schools should be enphasised. By denonstrating what has
been done, these conferences deaoastrate what could be done.

1. H.S.F. Grant CJ-281: Petar G. Lykos» Principal Investor 1968-71.

2. Approximately 400 and 200 respectively if Bates and teid (1971) are generalized.

3. Alaost none of the participants received release tiae froa their noraal nine to twelve hour
teaching load.

4. These prograas were developed as Coaputer Enriched Teaching Oait^. (CET0) detailing the
teaching probleas, coaputer prograas reguired, consuaer docunentation, and text material to
illuaiaate the principles treated in the prograas. CETU prograas were entered into our
cooperative Progran Exchange Service (COPES) library to facilitate distribution to other
schools.

5. Several program*; were exported to the University of .'nxas and the North Carolina regional
networks where they reportedly received soae use.

6. The computational laboratory concept proposed by lykos (1970) should be considered in soae
detail by sociologists since it aay provide cost-effective support for aost of the
innovative strategies proposed here.

7. See Anderson; 1971 for a survey of data analysis software*

8. Unfortunately these prograas have been cut back greatly in 1972 and none of the existing
institutes are helpful to sociologists in developing coaputer abilities. Heinstock, of
I.I.T. provides an excellent aodel of a suaaer institute for physicists.

FOOTNOTES

480

BBFEBEBCES

1. Aaderson, tonal d E. , "A Survey of Application Softvara For Social Data Analysis,”

£u£9tdiias at tit ataaii null (LQinmct at ggmttti ii mtoatuiitt amisaii#

Hanover, lav Hampshire, Tha Uaivsraity Fraaa of Bev England, 1971.

2. Anderson, Boaald E. , "A Survey of Applicatioa Softvara For Social Data Analysis
instruction," t£2££ ldlig« fit lit BiSfild lUlil SfiBlttflfif 21 CfiMlMi li tit Paderqr&duatt
Curricula. Hanover, lav Hanpshire, 1971.

3. Andersoa, Boaald E. # aad BcTavish, Donald C., "Sociology, Coaputara aad Bess Ondargraduata
Education," frocfaj^gs o{ g Conference qg goanutara 1b ill Undergraduate Curricula, Iova
City, Iova, The Univarsity of Iova, 1970.

4. Bates, Alaa P. aad Sua Titus Baid, "fit Sociology Bajor ia Accraditad Collages aad
Universities," (|f American Sociologist. fol. A, pp. 2U3-2U9, 1971.

5. Davis, Jaaes A., "Using IflPBESs to Teach Sociology,” Proceed i nun qt f|e Second iEBiil
g2Btt£tagS 2B C2iEBttU lB tit BBdUUBdBAtt gBttlSilt* Harover, Bav Haapshira, Tha
Uaivarsity Press of Bav Eagland, 1971.

6. Denk„ Joseph B. , "Curriculua Davelopaaat of Coaputar Usage ia Borth Caroliaa,” Proceed lean

°L i Coai£ESB££ PJ1 £S«£!lttM ill U* 2&dC£S£l £JltlASBiM» Io»* (itT» Io*,» Th«
University of Iova, 1970.

7. Francis, J., BcGinnis, B., and Schaell, B. , "Cospater-Based Instruction in tha Social
Scieaces - an Ezperiaental Course in Basearch Bathods,” Pyogaed jigs of § Conference op
Computers In tfre y§dafqraloate Curriculum. Iova City, Iova, The University of Iova, 1970.

8. Haablen, John B. , "Using Coaputara ia Higher Education: Past Becosaendaticns, States, and
Meeds," Consummations of tfegT ACB. fol. 14, Bo. 11, pp. 709-712, 1971.

9. Kreider, Glen D. , Sis, Francis B. , and Villiaas, Anthony V., "Instant Turnaround in

Instructional Conputing - Sole Eianplen Fron the Social Sciences at the Pennsylvania State
University,” Proceedi igs of a gQ|[BiB|g§ si ift the Undergraduate gurrtglae, Iova

City, Iova, The Univei sity of Iova, 1970.

10. Luehraann, Arthur H. , "Dartmouth Project COEXIST. Tha Coaputar Qua Coaputar,” Proceedings
of the second Annual Coaferenca on coppqters li f|e Undergraduate Curricula. Hanover, lav
Hanpshire, ~The Uaiversity Press of Bav England, 1971.

11. Lykos, Pater G«, "I ‘‘ter Token Acadenic Coaputar Use - Then Vhat?” Mugftloiil Still
Moveaber, 1970.

12. Beyers, Edvard D* , "IBPBESS and Undergraduate Education in the Social Scinnces,”
Proceedings qf a Conference op Coaputers ig £|e Undergraduate Curriculua, iova city, Iova,
The University of Iova, ?970.

13. O'Kane, Janes fl., "The Application of Enpirical and Coaputar Techniques to Undergraduate
Sociology Besearch Courses,” Proceedings of a Conference oji Computers in the Undergraduate
Curriculua. Iova City, Iova, The University of Iova, 1970.

14. Sia, Fraaces fl., Gordon F. DeJoug. Glen D. Kreider, and David Kaufaan, "Data Analysis for
Sociology Undergraduates: Iaaovations of Instaat Coaputation,” The A^yicay Sociologist,
fol. 6, Bo. 2, pp. 153-157, 1971.

IS.. Sia, Frances fl., Laurence S. . Bosea, and Glea D. Kreider, "Instant Turnaround aad
Conversational Coaputing as Instructional 7 joxS in the Social Sciences,” proceedings o{ the
Second khftual Cooferepcj og Compute s la f|£ Undergraduate Curricula. Hanovar, Bev
Hampshire, The Uaiversity Press of lev England, 197U.

16. Vargus, Brian S., and Douglas Bhite, "Beoort oa an Atteapt to Utilize Coaputers in Urban
Affairs Education," PtQcea jjnga of fhg second jpngf 1 Conference of Computer? li tbe
Undergraduate Curcicula7~fleaover7 Bev Hanpshire, The University Press of lev England, 1971.

17. tfildgea, Joha K., "Coaputers and Undergraduate Training in an Underdeveloped Area: The Case
of Louisiana state University in Bnv Orleans,” ££&cfsiliBS 2t the Second Annual conference
on Coaputers ig t|ft Undergraduate Curricula. Hanover, lev Haapahire, The University Press
of Bev England, 1971.

481

176

POISSON - k Daughter of Dartaouth's IHPBESS
a as Boob Bocd ia the Environment of
IBH TiB<t-3hariag

Joseph a. Desk

North Carolina Educational Computing Strrict
lesearch Triangle Park, North Carol i»a 27709

Telephone: (919) 549-8291

lliiaiafi iiZM

The faaed survey analysis system of Oartaorith College, Project IHPBESS 1 ], has been aoved
to only t vo computer centers outside of Dartmouth «s Rievit Center: to the Natal Academy (with a
near identical systea) 1 the onsr delivery of a disk, a ad to an IBH 360 Hodel 75 at the
Triangle Universities Computation Center, TOCC, in North Carolina. POISSON, £ackage $f
Instructional Social purveys gr gorth Carolina* vas bora zt TUCC ia a delivery closer to niae
months that involved no ease to the birth pains such aa the shipping of diaka or tapes, lhe
birth of POISSON provides not only a new system for survey analysis to people tiae-shariag oa
IBH 360 or 370 systeas but also a delineatiou of parameters involved in the "transportability”
process of interest to all vho are faced with this probleaatic area(2j. Transporting tutorial
developments and pedagogical advances along vith computer prograas to an entirely different
tine-sharing enviroaaeat ia both a financial necessity &ad a sine gaa non condition for
curriculua usage of tle computer to the vast aajority of aocial scientists vho are yet unable to
produce these syateas theaselves.

IHPBESS has a reaarkable history and has been veil docuaented in this seriea of coaferences
[3, 4, 5, 6). Not only has the systea developed to be a poverful tool for undergraduate instruction
in survey analysis but the student involveaeiTt in its evolution hvs provided, at leaat
theoretically, the base on vhi rh all educational developaent should ride, k studeit refined
systea operating on real data and pointing tovard significant research on the undergraduate
level offered an optiaua six of educational design criteria available in social survey syateas.
The North Carolina Educational Coaputiag Service (NCECS), aa NSF funded netvork involved is
curriculua developaent, produced POISSON m one year vith the goal of retaining aa auch of the
design criteria and current pover of IHPBESS aa possible. POISSON haa run on aa IBH 360 Hodel 75
and is nov operational os a 370/165 at TOCC. The entirely nev systea, POISSON, involved
transporting HO FNOGBAHS but a vast quantity of concepts, the docuaeatation of vhich
"transportability” is unavailable, to the author's knovledge, for aay educational syateas.
Liaitatioas of the daughter package are also essential to coaauaicate to those IBH users vho
desire a true picture of the availability of POISSON.

Nhat aay seea reaarkabJe to the potential uaer of POISSON is that a survey analysis syatea
couponed of prograas and data bases vas transported vithout any prograas or data bases from
Dartmouth being involved. Not even an algoritha vas adopted froa the IHPBESS aystea. k specific
rationale for starting froa scratch (vhat vould seea to be a vaate of tiae) vill be treated in
the nest section dealing vith the difference in the coaputer ayateaa at the parent and daughter
sites. Transportability involves aoviag aocial science, survey analysis, aad pedagogical
aethodology and not programs aad data baaes, strange aa thia aay aeea to the desperate searcher
of softvare. There are aaay super systeas to do survey analyses! 5 J but . f ev vith all the
necessary paraaeters for undergraduate education. The fact that fev of these super syateas are
used in undergraduate education coupled vith the historical truth that there is ao money in the
sales of softvare should indicate vhy transportability doesn't involve prograas. There ia no
noney in aoftvare because it is dovnright easy to prograa concepts once the difficult work ia
done- building the concepts. POISSON is a vitneaa to this fact.

Then vhy aove IHPBESS? The survey analysis aystea of Oartaouth ia the culmination of a
Billion dollara'[7] vorth of sociology, political science, survey analysis, pedagogy,
sophistication through developaent, ayateaa design, «.ni student interaction to aeatioa a fev of
the aerits. NCECS has spent less than 110,000 in building POISSON. "Traaapor tability” of the
systea can be categorized as follovs:

Survey Analysis
Social Science
Data Set Construction
Code Books
Systea Developaent
Tutorial Pedagogy
Student Feedback

ERIC

413

Survey Analysis: Aaong other founders of survey imljiii in undergraduate education, Janas
A. Oa? is (foraerly chairman of the Sociology Department of Dar .mouth) has provided a theoretical
and pedagogical foundation upon which IRPRESJ was built[8J. Tha approach kan a philosophical
basis vh'.ch projects that a student who is taught one sou-parametric statistic (tka ganna) vary
wall caa do significant analysis aad hypothesis testing on real data if ha has a systan by which
he can reach r<it’. data without getting sidetracked by conputers aad their jargon. To inport
IBPRESS is to inport this philosophy. Davis, flayers, and a student fron Oartnouth gave two
seninars to social scientists of North Carolina before tha anvironnent was considered prepared
for is philosophy. Davis1 book[8] has been adopted by at least one participating university,
indicating the inport of the philosophy itself.

Social Science: Any data set worth its salt is the result of good methodology and contains
too nany variables fcr undergraduate consumption, interest, or even relevancy (to say aothing of
systens imitations;. The largest IMPRESS data set, PBKS08, involves only 109 out of 550
possible variables. Subsetting these variables for undergraduate relevancy is social science and
a significant factor for consideration in transportability. The first two data set?: of POISSON
borrowed this work in toto (es well as several other IHPIBSS concepts).

Social science is also involved in building standard dichotonies and standard groupings for
each variable in order to provide ea*; first level analysis. The product of this work by social
scientists at Oartnouth is transportable.

A published priner[9] for the use of IBPRESS contains social science as well as systens
inf or nation. NCECS has aiso published a priner£10] which was not possible without the Oartnouth
version.

Oita Set Construction : Since XflPBESS data jets require an "inversion" of the original
survey fron respondent-oriented records to variable-oriented records, tha record fornat
resulting frou the inversion is an inportable iten. Systen differences require reconstruction
but the contents of the inverted records are that nuch easier to produce once available.
Purther, the problens in selecting educationally relevant data sets are reduced if those used in
XflPBESS are adopted. These problens obviously involve the availability of the data sets in the
public donain or in some consortiun arraageaeat (such as XCPI[ 11 ]) - sonething to consider!

Codebook: Significant survey analysis requires a reliable codebook for each data set, the
production of which is nost costly. Since 30 such codebooks are available fron Oartnouth at a
low cost (about $2.00 each) the use of these seens warranted at least for the data sets of
POXSSOH at use in XflPBESS. Xn starting up, PCXSSON adopted two IBPRESS data sets and their
corresponding codebooks: PRES68 (Presidential Election Survey of 1968 - SBC) and ETHIO
(Murdoch's Ethnographic Atlas E^nography Version). The traesportability of codebooks was
therefore essential to the whole process.

Systgp Development: The evolved XflPBESS systen was transportable by careful fullfillnent of
the systens requirenents on I8fl tine-sharing, with only the output of XflPBESS runs required, the
years of refinenent were translated into the POISSON version. Although POXSSOM has not as yet
the full power of XflPBESS, the open-ended nature of the XflPBESS systen is clearly discernible
fron output only and the preservation of this flexibility was felt to be necessary.

Tutorial Pedagogy: The interactive nature of XflPBESS has two tutorial thrusts: the instant
turnaround on questions to a data base and several adjunct nodules which teach the logic behind
this approach to survey analysis, instant turnaround on questions to r data base was not very
readily transportable and the conpronise represented by POISSON will be treated in detail in the
section below entitled "How POISSON Looks." The adjuact tutorial nodules are extr^nely inportant
to transport since they provide another significant resource for custjnixed teaching across a
vide spectrun of student backgrounds and learning approaches. Two progress, 2x2x2 and VOIDS,
were rebuilt to augnent POISSON.

Studept Fefcdbigk: To this writer, tutorial or interactive educational systens suffer
generally fron the absence of student feedback as a result of usage of a systen or even in the
design of the systen. IBPBESS is not guilty oc this onission and the interactive logic and
fornat reflect the heavy student involvenent in the evolution of the systen. POISSON van built
so that the output facing the user was as nearly identical to that of XflPBESS as possible in an
attenpt to transport this actively sought and Laceived student feedback. Again, it nust be noted
that the output of student runs and not prograns was the only need for transporting the package.

4~8

484

A LATHAM4 S ail Of STSfB IS DIFFERENCES
AT THE PARENT AMD DAthJHFlR SITES

The Host] well UUcictivt Sfitu (BIS) at on At DAruaotk supports tine-sharing slsost
exclusively. To is ssaas thst the vest aajority of cosputer runs Are subaitted through a keyboard
vith tke AASveie to reguests being delivered in a feu secouds so thst the ossr apparently i*
constantly in coaamicatioa wit A tAe conputer. TAe IBB 370 Bodel 1 (ssd our previous sachine
the IBB 300 Hotel 75) support a ties sAnring systen cnlled tAe Con vers a t ion a 1 ProgrAAsing Systen
(CPS) but tAis systen is sot tAe ssjor support feature as it is ir tAe HIS systen. •Ante A*
conputer runs vith tArnnroAAd tine averaging 30-60 ninutes tote up 75 percent of this nncAiue.
In genernl therefore, the rsnl power of the 1BH systens is in "natch'1 u»age ns contrnsted with
the "interactive" usnge in the HIS systen.

uhnt doen this nenn for the user? CPS users do not Ante the overall internctive cups city
avnilnble to BIS users. CPS not only Ass a lisitntion on Aou snay people con get on the
internctive systen nt tine (About 20 ns conpnred with About 90 on the DnrtnoutA BIS systes)
but the sise of software packages in CPs is also lisited conpareA to those possible in MIS.

On the other hard, the f»st core of the T0CC IBB systes is signif icnntly greater than that
available on the Dartaouth conputer and the batch systes cos so1* gently has far no re capacity for
handling large data bases and prograss. IBP1ESS is a tightly overlayed systen using a large
nuaber of external files. The batch systen at TUCC does not suffer fros this liaitation because
of its vo' use of fast core.

The initial problea is designing POISSOH was to preserve the interactive nature of IHPIBSS
as far as possible but to eaxiaise the use of the bstch power of the IBB systes. TAe design
features decided upos basically set op the isteractive systes to guide the ucsr toward
questioning a data base but restricted the actual calculations to the batch systen. Mot the
least of the considerations leading to this feature the relatively higher cost of
interactive coaputing versus batch coaputing, the foraer being on the average 2*3 tines aore
expensive than the latter.

Since a batch nystea was necessary to design , the BASIC league?* could sot be used for this
systen and PL/I was selected as the language of F0I5S0N. TAis decision necessitated the total
rebuilding of IBPRBSS since both the language and the aachiae differences aade eves the
transporting of algorithns iapractical and really ispossible.

Coupled with a batch systen is an interactive spates preserving tnc tutorial power of
IHPRESS. This systen was also rewritten is PL/I since this language is sore powerful than the
version of BASIC supported at TUCC. This decision was also required to facilitate the
coawunicatioa of the interactive systes vith the bitch systen.

Coaplicatiag any possibility of direct translation of IBP1ISS prograss into POISSON are tte
fundaaeatal aachiae differences is the two systess. TAe word sise of each aachiae is different -
an outcose of aachiae design. TAe staff at Dartaoath actually shaddered when the possibility of
algoriths transfer was suggested and this reaction was repeated by the NCtCS staff upon looking
at tho IMPRESS prograss.

BOM POISSON LOOKS

POISSOH does look alsost identical to IMPRESS when only output is seen. However, POISSOH is
actually foar independent systems*

POISON: Interactive Tutorial
POISSOH: Pull* Blown "BATCH* Systen
ADDER: Data Base Conversion Systes
2x2s2 6 MORDS: Adjunct Tutorial Units

POISON and POISSON together parallel the IBPRBSS systes and are s cosbisation f the United
isteractive CPS systes and tbe powerful batch spates at TUCC.

POISON <*lone looks alsost identical to the XHPRISS systes but it actually operates on a
very United file of oach data base. TAis interactive version gaidea the user with the ease
branching as does IMPRESS so that the EXPLAIN and DETAIL features for the novice are available.
POISON also provides all of the iuforsatioe possible on available data seta and the variables is
^each data set (along with the descriptions gf the variables and their categories). TAe user is
guided through the selection of grouping options for each variable (even the process of unking
his ova categories froa the raw data) and through the selection of . statistical options alsost
exactly as IBPRBSS does by senna of the. United file built specifically for each data set.

VAat POISON does. sot do is to follow up by anaverisg the gaeatioa posed to the data base -
it aerely outputs the properly foraulated question for a run into the batch spates, POISSON.
POISSON does the work and really can be used independently or even without ever going through

479

485

POISON. Once a user has gone through POISON one, two, or three tiiM, he can directly use
POISSON without tho tedius of the interactive-tutorial process and cam ash as usliaited auaber
of questions to each data base s\aul taaeously.

The coaproaise represented by POISON/POISSON has advantages and disadvantages, optisisatioa
of liaited teraiaal availability for interactive coaputiag becoaes a reality for the ssall
college users with less than a few terainals and too easy users trying to get as hour or so at
these terainals. The lowering of cost is also an advantage of going batch once the POISON
interactive systea provides the training for this. Dartaouth student feedback! 12] has indicated
that IHPBESS "experts* learned to by-pass the tutorial device in order to get into the "batch"
systea directly. This was a reaction against the tutorial tediua.

The ever-ringing debate over the educational advantage of alsost iaaediate answers to a
first hypothesis[ 13 ] points out a disadvantage of POISSON. The batch tursarousd is probleaatic
but the trade-off with cost and terainal availability sates POISSON sore than viable, output is
the current version oi POISON is a production of card foraats for input data to POISSON so that
students currently are forced to keypunch after running POISON- a two-step process. Direct feed
froa POISON into POISSON was sot possible with the version of CPS used up to January 1, 1972,
but the introduction of TSO (Tiae sharing Option) at this tine will sake the direct feed
possible and the second stage will be eliainated.

ADDER was built to Allow a new data set to be added to POISSON. The autoaation of this
process has opened the possibility of expansion so that four additional data sets to P1BS68 and
BTHNO are currently being adapted.

WORDS and 2x2x2 are tutorials dealing with analysis of the user’s own data for 2x2x2
contingency tables. These prograas not only teach gassa analysis but also allow the analysis of
available surveys froa the popular aedia and foraal publications, given the ability to group
variables as standard dichotoaies. Of course, these prograas run is conversational PL/I at TOCC.

LIMITATIONS OF POISSON

Of the two aain branches of IHPBESS, discrete and continuous analysis, only the discrete
path was aade possible in the first version of POISSON. This liaitation is only a result of
convenience since the addition of the second branch was decided to be developed after the
discrete branch becaae reliable and relatively debugged. Several other options were set aside
for a later version for a realistic beginning. The absence of a continuous branch aakes
regression analysis and sodeling as yet iapossible but Beyers of IBPBESS has indicated this
branch to be in relatively infrequent use.

IBPBESS allots user defined files to be built in order to save intersediate results which
subsequently would save repetition by the user. This file capacity is not necessary in a batch
systea and does not exist in the POISON interactive systes since no results are produced by this
systen. Several IHPBESS options related to this file savisg are not is the POISSON systea.

Table 1 lists the coaaands available in both systeas.

TABLE 1

Coaaands (Discrete Hode)

POISSON

MfKSS

XTAB

HABG

ASSIST

ITEH

SCALE

EFFECT

IDEA

STD

The ASSIST cossand is a tutorial considered unnecessary in the first version of POISSON. ITSH
(itea analysis), SCALE (Guttsan Scaling routine), EFFECT (effect paraseters) , and STD (test
factor standardization) were left to a second version. IDEA (coaputation of significant
associations) was left out due to tho availability of VOBDS and 2x2x2 considered to effect the
sane results, since HABG (Marginals) and XTAB (cross- tabula tion) are the work-horses of the
IHPBESS systes, the first version of POISSON was liaited to these coaaands.

480

Table 2 lists tbd "statistical options" available seder cross-tab elation for both POISSON
and IHPBISS.

TABLE 2

"Statistical" Options for XTAB

msm

wuss

DESCRIPTION

SELECT

Partitioning by inclusion

B EJECT

BEJECT

Partitioning by exclusion

o/o A

Table of percentages across

o/o D

Table of percentages down

o/o TAB

Table percentages on total

CHI

Chi sguare

DELTA

Table of observed sinus expected fregueacy

EXP

Table of expected frequencies

PBEQ

Pregnancy table

GAMMA

GoodadU and Rruahel's Gaaaa

NOTAB

Suppreasea all table output

Tule'a Q for dichotoaous data

rule's Q vith brief interpretation

Pearson's C

Soaer'n D

LAMBDA

Goodaan and Rrusial's Laabda

NOHTAU

Goodaan and Rrushal's Tau

OBDTAU

Kendall's Taa-ordinal data

PHI

Phi

Tschuprov's T

eraser's V

rule's r

Absent options in POISSON are a result of convenience and can be added later.

ACCEPTANCE OP POISSON AND ITS PDTUBE

POISSON has bees used in sose Nay in 10 colleges in North Carolina after only three aonths
of existence. Its quick acceptance vaa a result of vorkshop exposure and the preparation
involving Dartsouth personnel. It vill take at least a year sore before this acceptance can b*
analyzed vith regard to the package's reliability, to its preference over other syateas, to the
absence (to the user) of alternate s/ateas, or to its validity* One inherent advantage of
IHPBESS has been the ease by vhich a user can contact a data base vithout programing experience
or the need to digest three levels of annuals reguired by system exeapliried by SPSS. POISSON
should add criteria to test acceptance as a result of this advantage*

The continuous branch is projected for iapleaeatation in 1972. Other additions vill be aado
ad hoc* Pour data bases are being prepared for addition to the systea* future developaent vill
depend on the continuous acceptance of POISSON in a predoaiaantly batch enviroaaent already
powerful in SPSS and large statistical systeas*

The current version of POISSON has been exported to the University of Iowa and its network.
The batch systea reguires 167K of core and is in PL/I. NCSCS is eager to provide tapes
containing the entire systea (batch and intecaccive) as well as the two inverted data bases,
PBES68 and ETHNO to prospective centers having these ainiaua reguireeents.

BEPEIENCES

Interdisciplinary Machine £.ocessing for Research and education in the £ocir,l Sciences*
Edaund D. Meyers, "An Introduction to Project IHPBESS," Tine-Sharing Colloguiua, Kiev it
Coaputation Center, Dartaouth college, Pebruary 19, 1970.

2. Of hundreds of visitors to Dartaouth who were interested in aoving IHPBESS, the author
represents the only visitor to actually iapleaent the systea at hone* Private coaaunication

t froa Edaund Beyers, Director of Project IHPBESS.

3. J. A* Davis, "Using the IHPBESS Systea to Teach Sociology," Proceedings of the Second
Conference on Coaputers in the Undergraduate Curricula, pp. 382-388, Dartaouth College,
June 23-25, 1971.

487

4S1

4. B. 0. flayers, "Be Doa't Know What «e*re Doing," ibid, pp. 159-170.

5. B. Anderson, "A Survey of Application Software for Social Data Analysis Instruction," ibid,

pp. 135-141.

6. B. Dm flayers, "IBP1ESS and Undergraduate Education ia tke social Scieacas." Proceedings of
tha First Confaranca on Coaputara in tha Undergraduate Curricula, pp. 8.23-8.29, Tka
Uni varsity of Iova, June, 16-18, 1970.

7. Mo atteapt is aada by the author to total tha graata aada by aavaral foundatioaa aor tha

contributiona by Dartaouth to IflPBBSS. Boaavar, a aillion dollars ia by no aaaaa aa

exaggeration*

0. J- A- Davia, "Bleaeatar y Survay Aaalyaia,” Prantica-Ball (Bathods of social Science
Sarias), Englevood Cliffs, Bev Jaraay, 1971.

9. IBPBESS Staff, "The IMPRESS Priaer,” Sacond Edition, publishad by Projact IflPBBSS,
Dartaouth College, 1971.

10. N. flozlay and J. Devk. "The POISSOR Priaer,” publishad by MCECS, P. 0. Boz 12175, lesearck
Triangle Park, North Carolina, 1972.

11. Inter-University Consortiua for Political Beaearck.

12. Town fleeting ia Social Sciences, Second Confaranca on Coaputara ia Uadergr-duate Curricula,
Dartaouth College. June 25, 1971.

13. F. fl. Sia, Lm S. Bosen, and D. K redder, "Instant Turnaround and Convaraational Coaputiag
as Instructional Tools in the Social Sciences, ” Proceedings of tha Second Conference on
Coaputars in the Undergraduate Curricula, pp. 142-151, Dartaout’k Collage, June 23-25, 1971.

488

CORPflTVR AP PLICA TIO VS FOR SOCIAL SCIBRTISTS

J Thoms I. Kerahner

Onion College

Schenectady, Rev York 12.106
Telephone: (518) 346- 875 ^

There la a growing interest by collaga facalty aaabara nationally la coaputer application*;,
both in teaching and in research arua. This coafaranca and othara will provide raporta, ia may
disciplines, concerning innovations it coapatar use to achieve aaay adacatioaai objectives. soaa
new courses built around coaputara will ba added to the uadargraduata curricalaa. nany othar
couraea Jill iatagrata aiaulatioa aodala, hypothaaia taatiag, aad the Ilka lato aicltlag
couraea; thaaa coaputar-orientad applicationa will aeaaurably lacraaaa intaraat, relevance, aad
acadaaic content. Tba growing availability of tiaa sharing taralaala an wall aa data procaaaiag
facilitiaa inauraa that thaaa approachaa will ba open, at laaat potentially, to ev>ar-grovlag
nuabars of faculty and students in the yearn to cone.

A critical problaa is how to gat additional colleagues interested in aad knowledgeable
about quantitative, coaputar-orientad claaarooa projects, such coapotar projects add interest to
classes, il' they often enable instructors to deal with nore realistic problems. The problaa
turned on four parallel needs: 1) how to atiaulate undergraduate faculty to use coapater-
orientad applications in their teaching and claaarooa aasignnerts; 2) how to iafora thaa of the
aany ongoing aodels, siaulations, and related coaputer applications currently available
coaaercially; 3) how to suggest coaputar-orientad projects baaed entirely upon on-caapus
aaterlals they could assign to their classes; and 4) how to provida collaga faculty with the
naceasary quantitative background ao that they would be coafortabla in their role aa teachers
whan they introduced this aaterial.

How can these needs be aet? Several social scientists froa Onion Collaga and Howard
University, together with the Canter for International prograas of the Raw Tort State Depertaeat
of Education (1) , asked theasalves if they could design an experiaental pilot prograa that would
aeet the needs of college faculty aeabers with considerable interest but little or no training
in quantitative analysis, let alone coaputar applicationa. The answer, not unexpectedly, was
yes. The result was an intensive suaaer institute for experienced collage faculty, sponsored by
the Rev York state Education Oepartaent and held at Onion College in the suaaer of 1969; the
prograa was generally felt to be so successful that it was repeated la 1970.

The purpose of this paper is to offer a preliminary report on the achleveaents of thane two
institutes. Short-tern suaaer Institutes are widely recognised as a prlsary vehicle for
dissealnatiag new developments — both teaching and aethodology - f or experienced college
faculty(2). In the hope that these nay be eleaents of this prograa worthy of adoption elsewhere,
this paper will highlight both the gains and the special probleas these sejinars have
experienced.

gjaSifcjglfll 2M££U£*2

It is not expected that a short- tera institute could fully substitute for one or nore years
of gradmte training in quantitative aethods or coaputer applications. Pew faculty, however,
have the opportunity to return to graduate institutions for such training. An intensive, tightly
structured suaaer Institute can present the basic theories of quantitative aethods. It can
highlight and Illustrate a variety of their usoa, particularly as they are keyed to claaarooa
instruction. It seeaed reasonable to expect that a successful institute would have a
substantial lapact upon both the contest and the guality of undergraduate, and even graduate,
teaching. Institute participants would be able to offer new courses aad certainly widen the
quantitative, coaputer-orieutcd applicationa in current offerings. It wan also hoped that
institutes of this kind would have a significant lapact on the undergraduate prograas of each
participants* college, since a faculty aeaber attendiag the institute can serve an a najor
stlaulus and a source of assistance to colleagues as well aa students.

Re also expected that institutea of this type could have a significant payoff in terns of
research. The participating faculty have a geatly increased understanding of the quantitative
literature la their field. They would lino, through assigned probleas aad projects, have
acquired soae coapetence in using quantitative aethodology for their own research project a.
(flany participants brought their own data to the institute, aad over the course of the suaaer
learned several aev ways to analyse aad interpret it.) It should be eaphaalsed that a dosea or
aore faculty, over two suaaers, had developed real quantitative research skills by the end of
the prograa. sabbaticals or research grants can support additional foraal study for soae
faculty, and virtually every faculty participant had sufficient background to continue and
extend his quantitative , kills hiaself.

489

483

Ifci Etaatai

While the opportunities foe coaputer applications in undergraduate progress have grow*,
rapidly, a virtual prerequisite for widespread coaputer use is a solid grounding in statistics
aad quantitative analysis. The necessary aatheaatical background and techniques, however, are
not widely understood, flany social scientists, whether econonists, political scientists,
sociologists, or historians, received little or no training in statistics or quantitative
nathods, let alone coaputer applications, during their graduate training. It is difficult Tor
the sost conscientious faculty aeaber to aaater this theory os his own. Tet this quantitative
nethodology lies at the heart of such of the influential uork is tha social sciences; it lias
cose to be widely represented in the published literature. We recognized the need to develop a
progran where experienced faculty could acquire the quantitative tools that aust acconpany
coaputer* oriented applications and innovations.

What were the key eleaents that sost be included in such a progran? Put another way, how
such natheaatical background was required before participants could deal effectively with the
naterial and its coaputer applications? The progran coverage was also United by the short tine
period. A too~aabitious soainar, no natter how intensive or how carefully structured the
presentation, risks overvhelaing the students, so that they cannot work with such of the
naterial •covered. " We questioned how such coaputer progressing instruction the participants
should be given, and e also debated how such quantitative theory, as opposed to applications
keyed to illustrative data sets, should be esphasixed.

Based upon cur experiences during the two sunners, it sensed useful to sent twice daily,
for 1 1/2 to 2 hours each tine, for regular "classes," all held in the nornings. These were
typically infernal lecture nestings, often with frequent questioning. Thirty-sinute discussion
periods followed the "classes, 9 pvividing considerable opportunity for give-and-take, afternoons
and evenings were largely free for coaputer work and reading, though ve tried to have one
•aethods" seainar a week.

a detailed discussion of the topics covered during the seninar Is not central to this
paper (3). The aajor areas covered by the progran are highlighted below, however, as an
indication of representative topics.

In terns of specific coverage, the institute began by exaaining the foundations of
quantitative social science and the role of nultivariate causal analysis. Fr os the beginning ve
discussed the concepts of significance, association, and spuriousness) and the larger question
of the difficulties of distinguishing causal fros spurious statistical associations received
eaphasis throughout the seninar. a full presentation of statistical theory laid the groundwork
for such of this naterial. The topics covered included descriptive statistics, stressing data
presentation (histograns, cuaulative distributions) and statistical characteristics,
highlighting standard deviations, the nornal curve, chebychev"s inquality, and the like.

The general linear vodel was studied in sone detail. Since regression procedures lie at the
heart of such of the quantitative work, the institute fully discussed the assunptions underlying
linear regression and then exaained analysis of variance and covariance. We applied these
techniques, using prepared coapute* progress, to several data sets. This work was followed by
multiple equation dependence analysis, including sodcl building; this led to sinultaneous
equations, identification probleas, causal ordering, and estination procedures. Factor and
discriainant analysis were presented, as were sone nonparasetric statistics. Hany other topics
were considered for one or two days.

as to the specific role of the coaputer, ve found that it was highly instructive to provide
only a brief discussion of Fortran progressing, with such of this concentrated during the first
part of the suaae Participants learned to write their own progress, which had the special
virtue of facilitating their subsequent use of tine-sharing consoles. Generally, however, the
institute relied heavily upon sophisticated prepared progress both for the assigned exercises
and for the applications to each participant" s particular field. Instead, ve devoted sost of
this tine to inforaing the participants about particular coaputer applications, eaphasixing
projects they could adopt to their claasrooa need; aad shoving then how to prepare instructions
and data for the aany "canned" progress.

In sua, the twin concerns of the seainar were constantly stressed. First, ve tried to show
how a vide variety of quantitative techniques could be used, with conputers to answer questions
in the social sciences. Second, ve attenpted to provide enough of a quantitative background so
that experienced faculty would feel ccafortable in their role as teachers when they introduced
this nethodology to their classes.

490

ERIC

m g&EUsimu

The iutltiU was intended primarily for experienced faculty aeabers of collages and
universities who had generally coaplatad thair doctorates without aigaificaat traiaiag in
quantitative aathoda or computers. Participants vara selected froa several social aciaaca
disciplines, including ecoaoaics, political science, sociology, sad history. Siace inch of the
aathodology was coaaoa to tha foar fields, no oaa discipline van allowed to doaiaata the
ear/ollseat ia either year. Because of tha large nuaber of .applicants, oaly a bo at oaa caadidata
in five coaid be offered a place in tha institutes. Tha selection criteria iacladad tha
customary acadasic and professional gaalif ications, together with indications of strong interest
on tha part of potential participants, he vara particularly intaraatad ia stataaaats by the
applicants indicating hov participation ia the prograa would benefit both thair collages and
thair personal developaent. To strasa oar concern that tha prograa have a substantial iapact
upon tha corricalaa at tha applicants institution, va raqaastad that tha Dean of tha Faculty
provide a latter assessing both the caadidata and tha probable iapact of his participation upon
his departaeat's curriculua.

There are two priaary criteria that were used to judge tha af factivanass of tha suaaar
institutes, one was tha joint evaluation of staff and participants, at tha end of tha suaaar, in
terns of the af factivanass of tha prograa in aaating its objectives, ware tha faculty
participants able to satisfactorily understand and absorb tha guaatitativa tools, becoae
faailiar with coaputar usage and applications, and discover several ways in which this
aethodology could be used to enrich or ravaap thair undergraduate courses? Perhaps aora
iaportant, however, is to assess tha effectiveness of this type of prograa in terns of its
carryover iapact upon, tha teaching and professional developaent of the participants. Ifhat
actual, concrete applications have aaanated froa or been stiaulated by successful coaplation of
this prograa?

The results froa regular assigaaents, projects, both foraal and inforaal discussion between
participants and staff strongly reinforced our feeling that a tightly-integrated intensive
institute prograa could accoaplish our objectives. Host participants did possess n broad
understaading of guaatitativa technique*, aad they displayed thair understanding by covplating
several coaputar exercises using a variety of data sets. In classes and saainar discussions va
felt that tha participants becase faailiar with a broad sampling of tha literature. *e also felt
that, both through the foraal prograa and by learning froa each other, faculty participants
would be aware of the aethodological strengths and weaknesses of alternative techniques. In
suac the institute's staff generally agreed that the objectives of the prograa were realistic,
and that aost participants lived up to our expectations (4) •

evidence on educational carryovar is aora inferential. Nearly a doses participants reported
that they were able to (and felt coafortable in) introduce new, quantitatively oriented courses
in their disciplines. Regression studies were widely instituted. Several faculty, particularly
political science, successfully introduced siaulation exercises and behavioralist 'gases.* In
teras of professional iapact, at least five participants have written articles that rely upoa
their aevly-acguired aatheaatical training.

Ia short, there is considerable evidence that prograes of this type can be successful.
Conferences such as this often focus on disseminating new teaching developaents and coaputer
innovations to faculty who are already faailiar with the general approaches. »e also see the
need, however, to attract and train aany additional social scientists so that they, aad their
courses, can benefit fros these 'realistic* applications. Our experience at Union College leads
us to call for the spoasorship of aany aore opportunities for quantitative crainlng for
experienced faculty, whether along the aodel described above or in other foraats.

1. The foraal title of the State Education Department is The University of the
State of New York. As such, it should not be confused with the State University
of New York (SUIY) and its 70-soae caapuses, though it does have the
administrative responsibility for the SUHY systes as well.

2. Thoaas E. O'Connell, £&lAftflSSs * President's 2i$i (Urbana, 111., The

University of Illinois Press, 1966), pp. 24ff.

3. The author would velcoae corresponding with interested readers on both topics,
readings, and problea sets used in this institute.

4. To our knowledge this prograa was the only susaer institute sponsored by the V.
Y. state Education Departaent that was ever renewed for a second year.

£b« tillUs

FOOTNOTES

ERIC

491

465

TOUABD TUB OFTIIIAL OSI OP COflPQTBI SIBQLATIOHS IV TBACHIRG
SCIBITIPIC RBSIAICB STIATBGT

Jo ha B. Thurnoad aid Arthur 0. Croaer
Oiivtriitf of Louinville
Louisville, Kentucky 40206
Ttlcphoit: (502) 636*6107

In thla paper we will describe the use of coaputer aiailatioaa of advanced problaaa aa p*,rt
of the undergraduate axpariaaatal psychology couraa at tha University of Loninr/ille. Tha
problaaa vara conducted In a way aiailar to tha DATACALL gaaa ainulatlonn reported lent year at
tha Dartmouth Coafereace by Dr. lichard Johnnon[ 1 ] of Barlhaa Collage, and Dr. Daaa a. Raia of
tha University of Richigaa(2]. Soaa of tha coaputer ninulationn developed by teaching fellra at
tha University of Richigaa vara aaad to teach tha atudaata tha research atrategy they needed in
order to tachla tha aora advanced problaaa used in our course. Psychology 311 at tha Oaiveraity
of Louisville ia a three* hoar courts conaiatiag of four aactioas with a aaxiaua of 20 students
par aectioa. Bach of tha sections in taught by a different faculty nenber with tha aid of hia
ova graduate teachiag aaaistaat. Tha course in required for all uadergraduate psychology najorn,
aad they typically take the course during their second or third year after conpleting nix hours
of introductory psychology. At present, the course can be taken either before, after, or
concurrently with statistics.

Prior to introducing the coaputer aiaulationa this peat year, the undergraduate
experiaental psychology couraa was taught according to the traditional nodal of the elenentary
psychology laboratory. The student van regaired to read the areacn scientific subject natter
rather broadly — aaterial vhich did not stiaulate the atudent to pose questions or seek answers,
and aoat of vhich was only peripherally related to the classrooa activities And laboratory
exercises. The student conducted representative denonstration experinents that could be
perfOLaed within the two-hour class period. He practiced the prescribed laboratory techniques,
wrote up the results of the exercises in a prescribed fora, and received a grade based on these
reports and tests ained at assessing the degree to which the textbook aatetial had been
connitted to nenor/. Clasnroon activities consisted of lectures that involved the students
little, if at all, in the scientific thinking endeavors characteristic of the subject natter
area. Finally, the laboratory exercises, although perhaps discissed in class, did not follow as
logically deduced experinents that were sensing fully related to the students* reading and
classrooa activities.

Dr. John Thuraond, one of the courae*s regular instructors, becaae increasingly disgruntled
with this traditional approach to teaching students, and about two years ago decided that the
only way that students could learn to think like scientists vas by acting like then. It was
realized, however, that the student could not be afforded the opport unity for doing this within
the constraints of a three-hour laboratory course unless the process vas nade nuch sore
efficient by coapressing the tise diaension with ninulated experinents. The use of coaputer
siaulations as a replaceaent for the tiae~consuaing steps in the traditional teaching approach
peraitted the developaent of a new approach that focuses on activities that are fundanental to
the solution of real research problens.

The researcher usually has a considerable anount of inforaation about a research problen
before he begins hypothesizing the outcoae of experinents. However, he does not know what
aspects of his knowledge about the phenoaenoa are relevant to the particular questions he has
foraulated, and it is not until he h*s discovered the inportant relations between the variables
involved that he begins to distinguish the relevant fron the irrelevant. Thus, nuch of the
inforaation needed to deduce the experiaental outcones is generally known for any scientific
research problen, but it is "hidden” by a lack of perspective concerning the nature of the
problen. In order to get the students involved in the kind of thinking activities that a
researcher uses in discovering new relations within a knowledgeable fraaevork, they were given a
carefully prepared description of the research problen to be investigated. This description,
nuch like a greatly expanded "scenario" that vas designed to acconpany the DATACALL gane (1),
gives the student sone background on the problen and tella hin about the research that has been
conducted in relation to it. The relations between sone of the variables studied in
investigations of the phenoaenon described are stated quite clearly in terns of experiaental
results. The really inportant relations are suggested repeatedly in the description, but they
never appear conspicuously as ones that experineaters in the past have been concerned with
directly. These inportant variables are "hidden" in the sense that they are confounded with the
variables the past experiaenters have aaaipolated.

It vas planaed that the students would apply the knowledge they gained fron the problen
description to the investigation of the phenoaenon the use Ives by aeans of experinents sinulated
with the Psychology Department *s PDP-9 coaputer. This would put then in the position of an
actual researcher who nust consider carefully and analytically the inforaation at hand, using it
to deduce fruitful hypotheses. Based on Thuraoad*s preparation of these naterials, a feilot

493

486

faculty ■•star, A rthur Ccoitr, v«f about to begii vork 01 the ptogcm for ilnlatli) the
problens vhen ho ottoodod tko Dartnonth Conference and oot Dro. Jokoooo and Halo* Oo realixed
quickly that tho DATACALL gane and oonpater ainnlatioaa they vere uning vould bo ideal for
introducing oar otadonts to tho aoro advaacod probloaa vo plaaaod to une. Bning thoir progrhna
and nodifying thoa to bo rno oa oar PDP-9, tho aodol doaliag vith ochiaophroaia a ad too bao
doaliag vith inprinting (both dovolopod at tho University of fllchigan) voro a ood in a DAT! CALL
fornat noar tho boginning of oar coorso la tho fall of 1971* Tho ainnlatioaa voro handlod by
noana of a tolotypo in tho claaaroon coaaoctod to tho coapotor aoao diataaco avay. Thia approach
proved to bo roaarkably aoccoaafal ia toaching tho atadoata effective atratogioa for coadnctiag
experiments and intorprotiag results in coaaoctioa vith thoir investigations of tho aoro
advaacod probloaa lator in tho course.

Tho cospator sinulations onpioyod daring tho firat part of tho coorao alao providod an
appropriate and useful fornat for aiaalating tho aoro coaplox probloaa. Xn order to pernit tho
student to diacovor tho really inportant variabloa hidden in hia problen description, those
hidden variabloa voro not Hated and described for tho atodoat in relation to tho conpriter
sinnlation. Tho variabloa shovn clearly in tho problen description aa having boon stQdied by
previous investigators voro listed for selection in tho sinalatioa just aa they voro in tho
University of flichigaa sinulations (2), but there vas in addition an mZm variable. Xn order to
test his hypotheses about tho unknovn "I" variable, tho student specified tho aaao of tho
variable ho vishod to investigate, stated tho range over vhich ho voald pernit tho variable to
take on values, and then entered tho particular valve for vhich ho vented tho ooapator to
generate results. Along vith tho nano of tho variable, tho range, and tho value, tho atadoat had
to enter hia variable's code vhich ho obtained fron tho iaatractor. Tho particnlar coda
given to the student vas based on hia description of tho experineat ho vented to conduct, ;*nd
tho conputer put in the appropr -to effects depending on tho nunerical value of tho code, and
the range and value specified.

Before tho introduction of those aoro advanced probloaa vith conputer sinulations
containing unspecified variabloa, ell variabloa voro specified (in tho earlier probloaa), and
the student's task vas to deternine vhich variables had effects and hov big they sore. In tho
aore advanced problens, the student's task vas to predict tho effects of the specified variabloa
on the basis of the infornation in his problen description, and to fornnlate hypotheses
concerning the effects of additional Variables.

Guidelines for sivulation Problens

The problen selected for description and simulation nust be one that has been investigated
systenatically enough to have produced sone convincing hypotheses concerning the underlying
causes of the phenoaenon in question. That is, the students oust be given a background leading
up to this problen and enough infornation to ask questions and develop hypotheses. The
instructor nust be given the kaovledge of hov the aechaaisn vorks (or relevant concepts) aad
vhat crucial studies led to its elucidatioa. The concepts elucidating the phenonenon under study
nust be relatively sinple and straight! rvard. The subject shonld be interesting to the
undergraduate student— i.e. , if not "relevant” to those aspects of hunan behavior involved in
today's problens, it should at least have sone inportant in plications for hunan behavior
geaerally. not only should the concepts underlying the phenonenon be kept to an absolute
nininun, the logic leading to experinenta that vill produce the concepts should be crystal
clear. The problens used in a course should be at different levels of difficulty, vith the
easier ones tackled lirst. Finally, the problen descriptions and conputer sinnlations should
serve as the vehicle for introducing the student to current knovledge of sone of the inportant
concepts of his discipline. Xn the undergraduate psychology course at the Osiversity of
Louisville, the problens developed led the students to consider nechanisns of enotion and
notivation, short- tern and long-tern nenory, and selective attention. These criteria are
characteristics of the sinulatioa problens developed at the University of Bichigan, and thia, no
doubt, contributed to the success of the tvo used in the first part of our course.

Description of Advanced Problens Developed fgp Course

Tvo problen descriptions and conputer sinulation pro grans vere developed and used in the
course. A brief description of then is given belov. (1) PAT BATS AND PLUMP PEOPLB. Bhy do fat
subjects, rat or hunan, eat nore than nornals when food is easy to get at, but loss than nornals
vhen the situation nakes it a little herder to get at the food? Actually, there are a nuaber of
interesting facts about obese hunans and rats vhich shov coincidence of behavior. It is not
surprising that obese hunans and rats eat noro "good" food than nornals. But it is surprising
that the obese, both hunan and rat, eat loss than nornals if the food is not too appetising even
if it is the only food available. Asoag the factors that can be related to eating behavior and
obesity are the effects of taste, prelo&diog vith food (i. e. , hunger), food visibility, prior
taste of food, the proninence of food cues, and frequency of eating. The extensive literature
concerned vith eating behavior of rats vith brain lesions vhen related to the hnsan data is

487

494

bidiaaiDf to saggest that the obMit y of cats 'ad asa aay kava a cosaoa physiological loess ia
thf veatroaedial hypotkalaaas. (2) Til COCKTAIL PAKTT FKOBLKH. «ov do «• cscogaits skat oas
parson is saying when otkscs acs speakiag at tks saas tiae? A us abac of possible siplaaatioas
foe this pksaoastoa aigkt bo explored, aaoag tkoa boiag tkoso colatod to lip-readiag, ges tares,
and tko lit#, tkoso that colato to difforoacos ia speakiag voices sack is aalo asd feaalo,
loudness differences, pitches, acceats, location relative io the listener, and differences
related to traasitioaal probabilities ia the subject aatter aad syntax of the language.
Investigations of the pkeaoaenoa in recent years have been conducted within the fraaevork of
theoretical foraulatioas eapkasising aechanisas underlying selective attention aad aeaory.

Prograanlpu Consldecatioas

The eatire set of progress used were written ia fOITIAI If aad were based upon the fora
described by Sain. (2). Considerable re- prog running was necessary to allow the programs, rua
originally on an IBB 360/67 with 1.5 aillioa bytes of core, to be rua ia a aackiae with 6K words
of core. The effect of this was to aake the prograas even a ore aodular than before, but
depeadiag heavily upon the overlaying capability provided by the auauf actarer.

The fora of the prograas was identical: a aain prograa called ia each of four links ia
succession, with ten subroutiaes distributed aaong these links. la order to convert a prograa
froa one experiaeatal aodel to another, it was accessary to aodify the subroutine that read ia
pnraaeters aad the subroutine that actually contained the aodel. Ia addition, soae shifting was
usually needed to coapress the prograa as auch as possible.

Presently we have five prograas working that can be aade available upon regaest. Two aore
prograas are ia the process of being written, and all seven will be converted to the BASIC
language this spring, for use on a tine-shared coaputer which has becoae available.

BialHaUflft 1EE E21S&

The advantages of using coaputer siaulatioas to stiaulate student interest aad
participation ia designing research was reported at the Dartaouth conference last year by Drs.
Johnson and Bain, our use of a siailar approach incorporating aore advanced probleas and
siaulations has substantiated and extended their findings. The students accepted the coaputer
siaulatioas as validly reflecting :he phenoaenon under investigation. In fact, they tended to
view the coaputer as "oanipotent* aad exhibited little patience with any constraints iaposed oa
the experiaents they wanted to conduct. By the end of the course, the students typically showed
a preference for designing their own experiaents, which were in aany cases sore sophisticated
than those peraitted by the coaputer siaulation. For exaaple, they wanted to aake inferences
that could not be aade on the basis of aeasuring the aaount of food eaten by huaans and rats
under various experiaental conditions.

The advanced probleas forced the students to think a great ..ore about what they were
doing in the coaputer siaulations and why they were doing it. Their ability to coapletely ignore
the inforaation they had been given about the variables in the siaulation was astonishing. They
resisted having to engage in any serious thinking about the variables involved, and wanted to
deteraine effects siaply by aanipulating the variables in the siaulation. Thus, the aore
advanced siaulatioas with aore coaplcte problea descriptions and unspecified varinbles forced
the students away froa aanipulating variables and aore toward thinking like a researcher.

Proa the instructors* point of view, the coaputer siaulations provided the stiaulatioa and
facilitation needed to improve their teaching effectiveness. This becaae very obvious early in
the seaester on the few occasioas when the coaputer was ”d*»wn", and a class discussion was
substituted for the coaputer siaulation. These discussions ceuteiad or what we would do if the
coaputer were available for the siaulation, and this led the students to a auch aore careful
consideration of their research designs. The use of the siaulations also precipitated
considerable discussion aaong the instructors and teaching assistants concerning what they were
teaching the students and how effectively they were doing it. Soae of the advantages for
iaproving teaching that the approach offered in our course were outstanding:

1. The students get a great deal of practice in deciding on research designs and drawing
conclusions using statistical techniques.

2. The coaputer, coupled with problea descriptions, peraits the students to siaulate aany
experiaents in order to discover new knowledge that they seek.

3. , Deficiencies in the student9s grasp of the essentials of statistical inference, effective

research strategy, & d knowledge of relevant aaterial are iaaediately apparent. Thus, the
coaputer siaulations provide an on-going diagnostic tool peraitting the instructor to clear
up the student #s conceptual probleas as th^ey arise.

495

4. Th laatroctor1! ef fectlvoaeaa la cltariag n the atadaat' a conceptual deficieaciea are

iaaedlately appac«Bt*i.a,f if tk* atadtat doaa aot aadtrataad vkat he la loiag* he doaa

aot approach tha coapatar aiaulatioaa intelligently.

5* Tha approach stiaalataa attaapta to apail oat bahavioral objectives for aach atap ia tha

coarae, and to aaka a raall y hoaaat avalaatioa of vhat tha atadaat ia learning.

Oa tha baaia of oar experience vith tha advanced problaa daacriptioaa aad coapatar
slaulationa, va faal that two gueatioea looa that aiat ba aaavered ia tha aaar fotara. Tha firat
one daatnda an ansver coacarniag exactly vhat it ia that tha atidaata ara laaraiag. Certainly
tha atadaats hava ao idaa. Typically, they hava had no axpoaura to coiraaa that require thaa to
do auch thinking, and thair idaa of effective laaraing ia tha coaaitaant to aeiory of yaat
nuabara of intarasting and iaportaat facta. Our attaapta to avalaata tha atudaata vith a pid-
tera and final axaaination aat vith aarginal aaccaaa at bast, indicating that oar appreciation
and andorstanding of tha laarning procaaa angandarad by tha approach ia, at th Ji point,
rudiaantary. Tha axaas va gava aaaaad to hava a lot of faca validity. They dafiaad aad
discasaad a problaa araa for tha atadaat, aad iacludad pacta that ragairad tha atadant to
foraalate hypothasaa, dealgn experiaenta, pradict aad avaluata altaraativa oatcoaaa, explain

positiva and nagativa rasulta, and craata aotira raaaarch prograaa for iavaatigatiag tha problaa

with accoapanying dascriptions explaining his raaaarch atratagy. Va axpactad that tha rasalta of
these axaas would correlate highly vith tha student* a ef factivanasa in conducting tha coapatar
siaulations and participating in claaa dl"cuaaiona. Vhlle tha axaas did a fair job at tha
axtraaas (for tha bast and vprat atudaata), tha reailta for tha aost part vara equivocal.

Parhapa tha lack of correlation is due to tha foraat of tha axaa aora than to vhat it vas

designed to aaasura - i. a., tha use of a vrlttan tlaad axaa an opposed to soae sort of oral,
self-paced procedure. In any ca^e, it la apparent that aora vork ia tha future vill ba necessary
to dataraine hov to adequately assaaa tha student's scientific research atratagy.

Tha second question coacarna tha atudanta* axpoaura to "live” daaoaatratioaa aad data
collection. Tha aain difference batvaan tha approach used ia tha courae described ia this paper
aad the one aaed by Drs. Johnson and Bain [1*2] the substitution of tha advanced problaa
dascriptions and coapatar slaulationa for tha student's ovn research project during tha latter
pact of the course. Vhlle tha use of these advanced probleaa introduced nav levels of thinking
and analysis for the studanta, about tvo-thirds of tha vay through tha courae tha aeceaaity and
desirability of exposing tha atadaats first~haad to tha phanosaaon under study van fait rather
acutely. Hence, prior to conducting tha cocktail party problaa, tha atudaata vara exposed to
prepared tapes vhlch daaonstrated aelactiva listening phenomena, and they participated in a
brief but instructive shadoving experiaeat. This pre~exposure aada tha cocktail party problaa
description and siaulatad experiment* auch note interesting aad ueaaiogful for the students. On
the basis of the success of this exparianca, ve plan to aaka aach of the siaulations used in the
future aore aaaningful for the students by thin sort of exposure to the phenoaenon under
investigation. By selecting experinents and deaonstratlons that require a alniaua aaount of
tiae for data collection, aad by peraitting tha students to analyse thair data collected oa tha
coaputar, the tiae devoted to this aspect of thair instruction ahould ba veil spent. Thus, one
approach concentrates entirely on research atratagy and coaputar siaulatio. j vith no data
collection during tha first part of tha course folloved by the student's ovn project vith data
collection during tha second part of the course (1,2). our approach concentrates on
Increasingly difficult coaputar slaulationa vith data collection and daaonstrations designed to
enhance the student's appreciation and knovledge of each problaa. Future vork ahould be carried
out to detaraine the relative aecits of these tvo approaches.

REFERENCES

1. Jcanson, t. DATACALL: A Coaputer-based Siaulatlon Gaaa for Teaching Strategy in Scientific

Research. Proceedings of the Conference on Coaputers in tha Undergraduate Curricula,

Dartaouth, June, 1971.

2. Sain, D. B. , & Head, S. Coaputar Siaulations in tha Bleaentary Psychology Laboratory.

Proceedings of the Conference on Coaputers ia tha Undergraduate Curricula, Dartaouth, June.

1971.

489

496

A 9IIX0US Gk HI AS a IHTIOD9CTXOR TO URIAH PLAHRIRG

Aaron fl. Koastaa# John Bartuolonev# and Judith Johnston
Ths Linden wood Col lagan
St •Charles, Missouri 63301
Talaphona: (J1 4) 723-7152

Introduction

All freshaea stndants at Tha Liadestood Collages ara required daring their first year to
take what is callad tha Liadeavood Conson Course. Tha statad pnrposa of this conrsa is to antics
thlse frashnan# individually and collectively# to coosidar what tha Connon Coursa faculty
believes to be the pressing probleas of twentieth century nan. Tha coarsa considers such issues
asecology- tha urban crisis# changing social values# nbortion# etc. During tha 1970-71 acadanic
year one broths foci of tha Connon Coursa was urbas planning. Tha pedagogical vehicle used to
iatrodece tha students to considerations which enter into tha planning of a city was an urban
planning gaae callad feu Town. In this paper tha gaae vill be described and tha pedagogical
results of asing Raw Town to introduce students to urban planning vill be discussed.

Iba fiAtt

Haw Town was originally developed by Barry Lawson (1) while ha was a graduate student at
Cornell Oeivernity and was expanded and aodified at Lindaawood. As originally designed# all of
tha playing and accounting ware dona by hunan participants. Re found these accounting procedures
tedious and tiue-consuuing for the hunan players; therefore we conputarizad tha gaae.

Plaiers

Tha players of tha gaae divide thenselves into five teans. Pour of the teans represent
developers aed the fifth represents the peblic planner or city nanager.

EilUSI3

The purposes of the gane are threefold. The first is to develop a city on the available
land. The second is for the developers to get the largest possible return on their investnent.
The third is to develop a city that is worth living in.

As night be expected# the fulfillment of this last purpose is nainly the responsibility of
the public planner# but the developer'; are involved to a lesser degree by neans of a "goodness
test" built into the gene.

Gane Board

The developnent of the city is done on a gane board (see Pigure 1) which represents the sap
of the land set aside for the new city. As can be seen in Pigure 1# the land has already been
divided into blocks# each containing four parcels of land.

The developnent land contains a lake# a river# and a railroad track# which are intended to
be forces is shaping eventual developnent patterns. All the land is assuatd initially to belong
to the bank.

mill

The developers have a choice of building resideaces# retail establishments# or industries
of varying sixes and densities.

The public planner is responsible for the developnent of parks# utilities# schools# the
town hall# fire stations# sewage pltnts# refuse disposal plants# health clinics# civic centers#
and airports. These units have fixed developnent costs.

in £111

Bach tean of developers begins the gene with $1#50Q#000 in cash. The public planner starts
with no noney# a 6300,000 debt Unit# and n potential incone froa taxes on the cuaulative vnlue

497

4S0

FIGURE 1.

Diagram of Flaying Board

491

498

of the property developed. The noreal tax cate is tee percent of the cumulative value. Play
occurs in rounds designed to simulate the activities of ore year of urban dmvelopmmtt.

Bach round starts with each of the teaas purchasing up to five pieces of land by snbsittiag
sealed bids. After tue land is purchased* the development phase of the gase begins vith the
developers bidding md putting up development units* residential* retail* and industrial. The
team representing the public sector can put up any developments consistent vith its income* its
debt limit* and the fines imposed by the public issue aspect of the game to be described
subsequently.

The rules for development sere designed to mirror the constraints on development present in
a real urbaa environment. For example* industry built on vater and/or rail lines earrus higher
income since transportation costs are lover; retail units in shopping cemterc are aore
profitable; rentals are higher on residences built on lakefront or park-front property* etc.

Developers are alloved to do the things they vould be expecte* to do in real life. They can
borrov noney* vote to raise or lover taxes* redevelop* raze their de velopnents* bribe city
officials* or band together to develop. The planner* on his side* can expropriate property, put
up public developments* play the developers against one another by promising to build cc not to
build* etc.* all presumably for the stated end of Baking the city the best nround.

At the und of each round the information on sales* developments* noney transfers* loans*
rectal* and tax rates are coded onto cards and fed into the computer. The computer analyzes the
events of the round* does the accounting for tha private and public sectors* and produces a
report sheet for each tean. The accounting is done according to the eguations given in Figures 2
and 3r vhiie a sanple account sheet is shown in Figure 4.

"joodaess Test”

The "goodness test” is designed to illustrate to the players the probleas that arise in
developing one piece of property vithout considering the effects developaents have on one
another. This is done by having the computer calculate the number of jobs available from the
industrial* retail and public developments as veil as the number of vorkers living in the
residential developments. If these two numbers are not the same* vithin certain tolerances*
penalties are assigned to the developers in the form of lover business incomes or higher tax
rates* depending on the direction of the imbalance.

Annual Investments s Land Costs + Development Costs
Cumulative Value - Sum of Annual Investments

Expend it tires = Annual Investments + Rents Paid + Redevelopment Costs +
Taxes + Bank Loan Interest

Money Left Er.rni.ng B»nk Interest (MEEI) s Cash-on-Hand from Previous Round

Expend i tures

Annual Income - Residential Income + Retail Income + Industrial Income +
.0?) * liEBI + *• i teres t from Private Loans

Net Income *» Annual Income - Expenditures

Cash-on-Hand - Cash-on-Hand from Previous Round + Net Income - Bank Loan
Ou ts tanding

Rate of Return = Annual Income ~ Tax - Rent - Redevelopment Costs - Bank

Loan Interest _

Cumulative Value + Cash-on-Hand

FIGURE 2. Accounting Formulas for Ptivate Sector

er.

499

4S2

Public Revenue - Tex Rite • Total Cumulative Value of Four Developera

+ Balance from Last Round + Intereat on Private Loana
+ Money froai Private Loan (or Gift)

Intereat ■ .05 * Amount of Bank Loan

Expendlturea a Land Costa + Development Coata + Operating Coa ta + Intereat
+ Redevelopment Coat + Rent + Penalties

Net Income * Public Revenue - Expenditures

New ’''nk Loan a Old Bank Loan - Net Income

FIGURE 3. Accounting Formulas for Public Sector

ROUND 1

LABOR FCaCE - 34.2 JOBS AVAIL. “ 103.0 RATIO LABOR/ JOBS - 0.33
INSUFFICIENT LABOR FORCE. BUSINESS INCOME REDUCTION - 66. 7 PERCENT.
TAX RATE - 10.0 PERCENT

DEVELOPERS REPORTS, ROUND 1

TEAM NO.
1
2

RES ID.

BUS.

TOT.

TOT. ANN.

TOT.

NET

CASH

BANK

CUM

RATE OF

INC.

EXP.

INC.

LOAN

VALUE

RETURN

32000.

41836.

115836.

600000.

660000.

-544163.

955837.

600000 .

3.5

75000.

1575000.

4.7

75000.

1575000.

4.7

30000.

47813.

123938.

525000.

577500.

-453561.

1046438.

525000.

4.5

PUBLIC ACCOUNT

REPORT,

ROUND 1

TAXES COLLECTED
TOTAL REVENUE

DEVELOPMENT COSTS
OPERATING COSTS
INTEREST ON LOAN
LAND COSTS
REDEVELOPMENT COSTS
PENALTIES
RENT

TOTAL EXPENSES
NET INCOME
BANK LOAN

BALANCE IN ACCOUNT
DEBT LIMIT FOR NEXT ROUND

112500.

260000.

52000.

10000.

322000.

-209499.

210000.

500.

281250.

THE PUBLIC ISSUE FOR THE NEXT ROUND IS FIRE STATION.

FIGURE 4. Semple Accounting Sheet

ERIC

493

500

EJlfeUc IMA S

At the end of each round the computer analyzes the "character" of the coaauaity already
developed and, on the basis of this analysis, decides which type of public development the
community needs lost. This development is then designated as the public issue for the next
round, and the public planner is fined one-quarter of its development cost for each subsequent
round it is not built.

The students taking the Conon Course were divided into nine groups each containing
approximately 25 students. The faculty who plans and teaches the course includes three net: berm
from the social sciences, three from the humanities and three fron the natural sciences. The
acadenic year is divided into four tine periods of about seven weeks in length. By rotating the
nine student groups aaong the nine faculty nenbers it becomes possible during the first three
time periods for every group of stadents to spend one seven week tine period being taught by a
social scientist, one being taught by a humanist and one being taught by a natural scientist.
During the fourth tine period the students work on independent projects to be submitted at the
end of the year.

The students played New Town one day, usually spending five to six hours on the gane,
during the tine period that thei*; group was being taught by a social scientist.

The actual administration of the gane was done by the staff of the Coaputer Center, two of
whoa, the director and a student assistant, are authors of this paper. After the gane was
concluded, one of the coaputer staff, in concert with the Connon Course faculty nenber
responsible for that group of students, would spend approximately one-half hour discussing the
results of the gane while it was still fresh in the students* Binds. Students were encouraged to
see relationships between the city they had developed in the gane and the characteristics of
existing cities. Such natters were discussed as the relation between transportation facilities
and development of the city, reasons for high concentrations of industry in certain areas of the
city, and interrelationships between the locations of different types of developments. The
Connon Course faculty nenber was then able to use the experience with the gane and the
discussion following play as a springboard for greater in-depth examination of urban planning In
the classroon.

During the acadenic year the game was played nine tiaes^ once with each group of students
in the Connon Course. It should also be noted that each of the social scientists on the Connon
Course faculty was involved in supervising a student group playing New Town three tines during
the acadenic year.

Further Use of New Town

During this sane acadenic year one of the authors, who was a sociologist on the Connor
Course faculty, was also teaching a course in urban sociology. The students in this course were
mainly upper classmen majoring in sociology. It was decided to use New Town as an educational
tool in this course. The contrast between our experiences in these two courses will be discussed
when our results are described.

The coaputer system of The Lindenwood Colleges, which was used for this game, is an IBM
1130 Model 2B, 8K core memory with one disk drive. It is also equipped with a 1442 Model 6 card
reader/punch and an 1132 line printer. The account forms were produced on the line printer using
five part paper, so that each of the teams received a copy of the Accounting sheets at the end
of each round.

Sol® of the Computer

In our judgment the use of the coaputer makes a crucial difference in the pedagogical value
of the gane. The emphasis in the computerized game is on the role playing in an urban planning
situation rather than on the tedium of doing the arithmetic. (It would probably take most
students up to one-half hour to do the accounting for each round. The coaputer analysis of the
sane data is essentially instantaneous) •

&£ Ms sl Ms Gate in ihe go .■■SB £M£3g

The Computer

501

484

It is also possible to change tbe conplexity of the ecoaosic node* used ia doing the
accounting without appreciably altering tbe tiae tbe coapeter tabes to aaalyxe tbe data produced
after each round. For exanpie, it could easily be arranged for part of the gane to be played
without the "goodness test" and part of the gane with this test to illustrate the effect that
the test has on the rates of return and the other econoaic neasnres of the success of
developaent ache a es.

AtiitMg al test iiaiaJkiB

Since the Coaaos Coarse is tahen by the entire freshnaa class, the students vho played lev
Town were of widely different philosophical and political persuasions. Sons began playing the
gane with positive attitude, full of curiosity about what night happen. Others felt that having
to spend a whole day on lev Town was a great inposition on their personal freedoa.

Despite the different initial attitudes, once the students got involved in the gane, they
seeaed to enjoy the experience. Many wanted to continue playing even after the allotted tiae
was spent, it is our experience that the serious gane approach to learning hns the & priori
advantage of being fun. It see ns self-evident that a learning experience which is enjoyable is
potentially nore effective pedagogically.

Hew Xflwn §5 a Learning Experience

The crucial question, of course, is whether the students learn anything fron playing the
gane. A further question is whether the serious gane has any advantages as a pedagogical tool
over other types of learning techniques.

The authors are fully aware of the worb of J. Skarac and D. less (2) which attenpted to
neasure quantitatively the learning value of a serious gane approach to learning, le have no
quantitative statistics to refute their findings that there appeared to be no quantitative
advantage to the gane approach.

our qualitative experience, however, supports the contention that the advantages of the
serious gane are not in teaching about the interplay of concepts when applied to a nodel of the
real vorl^. For exanple, the neaning of natural depreciation of the value of a developaent, on
one hand, and taxation on cuaulative value on the other, can be taught separately in the
classrooa. However, the effect on the tax base of the city of having depreciation on existing
developnents and insufficient expansion of the tax base through new developaent is better
denoustrated in a gane situation. He believe that Sharac and luss did not put enough eaphasis on
learning about interrelationships between basic concepts. Hheu these interrelationships are
taben into account the advantages of the serious gane becoae apparent.

our sanple was too snail to have control groups and to do extensive testing of the learning
accoaplished. The above nentioned convictions about the positive value of the gane experience
cone fron seeing students with essentially ac nore background than playing the gane five or six
hours becone able to discuss sonewhat knowledgeably the rather conplicated intertwining problens
facing the urban planner.

Our experiences with lew Town have deaonstrated that the following set of factors affected
the efficacy of lew Town as a learning experience.

The Connon Course faculty who supervised the student groups playing lev Town during 1970-71
cane fron three different disciplines within the social sciences: psychology, econoaics, and
sociology, is it turned out, these three instructors had varying degrees of connitneat to use of
New Town as well as to discussion of urban problens.

One of the authors, vho also taught the course in urban sociology which used lev Town, was,
of course, very interested in using the gane to as full an extent as possible. Befor* playing
the gane, his students spent tine discussing the principles involved in urban planning, and
received a prelininary introduction to the gane. after the gane was played, his groups d’scussed
the results in the classroon.

The other two Connon Course faculty were not so connitted to the whole lev Town endeavor.
They had participated with the entire Connon Course staff in deciding to use lev Town but urban
planning problens were not of great personal interest to then. They did net spend extra tine
before or after their groups played the gane ia discussing the gane or what the whole lew Town
experience was about, nor did they participate with their students in playing the gane. They

502

depended on the gene and the brief discussion which followed at the Coepntec Center to he the
conplete learning experience.

Our observations indicate that these varying faculty attitudes were passed on Co the
students in their respective groups, ill the student grourn learned s&netking fron playing the
gane, but the learning appeared nore extensive anong those groups of students who sensed a
connitnent on the pert of their instructor to the issues involved. Even the attention span of
the students during the explanation of the gane rules was narkedly greater for those 5 ho knew
that their instructor cared about the results of the gane.

He believe that the inportance of the attitude of the instructor night be overlooked in
evaluating any learning technique and especially one as conplicated as the serious gane. To us,
it seens crucial that the gane experience be one which the students and the instructor share
together or it ceases to be neaningful to the student.

££S£2Mli°A Si Students

The fart that we were using Mew Town both with freshnen in the very generalised Connon
Course and with upper classnen in a specialized urban sociology course allowed us to conpare
these two groups and the results of their using the gane.

These two groups differed in a nunber of ways. The upper classnen, it can be assuned were
nore sophisticated in their approach to learning as well as nore counitted to the study of urban
planning problens. The students in the sociology course did not cone to play the gane cold as
did nost of the freshnen. The sociology class had reviewed the rules of the gane and had
actually played a kind of warn-up gane of Mew Town before they began playing the gane in
earnest. The rules of Mew Town are adnittedly conplex (the full explanation of the gane
coaprises twenty printed pages), and not having the rules clearly in sind prevents a player fron
exercising freely all his gane options.

The following differences were noted in the two student groups. The freshnen, having less
preparation, exhibited greater changes of attitude as a result of play. They were dealing with
concepts which, in the sain, they had not dealt with previously in the classroon, and about
which they knew little. Their discoveries of the interplay between the concepts and values
enbedded in the gane were nore striking and had a nore dranatic effect on their understanding of
the problens of the real city.

The upperclassnen also learned fron the gane, but the gane served nainly to reinforce t'leir
understanding of ideas which had already been considered in class. Therefore, their ultinate
understanding was deeper and nore profound but the change fron their pre-gane to post-gane
attitudes was less striking. This nore profound understanding of the principles involved allowed
these students to play what night be terned a tighter gane. That is, in playing their gane, the
teams of upperclassnen nade better use of the econonic and political forces present in the
sinulated developing city. Their noves sere takeu less at randon than were the noves of the
teans of freshnen, since the freshnen were less sare about the consequences of each nove.

Bealisn ip Mew Town

There appears to be a lack of agreeaent anong the designers as well as anong the users of
serious ganes about the inportance of realise in the gane rules. To illustrate, in the case of
Mew Town it night be discussed whether the quality of the learning experience is affected by
giving each tean of developers $1,500,000 as an initial sun of available capital for beginning
their developeeet, instead of $1,500 or $150,000,000. Since it is a gane, does the anount
natter?

The authors believe that in order to use the serious gane as a vehicle for teaching about
the real world, the context in which the gane is played should be as close as possible to the
context in which the activity the gane is designed to sinulate is carried out in the real world.
In our case, our purpose was to go directly fron playing the gane into a neaningful discussion
of urban planning problens in the real world. For this to be possible it seens self-evident that
an attenpt nust be nade to nake the gane as realistic as possible.

He cannot pretend tuat all the aspects of Mew Town correspond directly to features present
in an actual urban planning situation. He are aware of several urban planning and land use
ganes, such as CLU6(3) , which are in nany ways nore realistic than Mew Town. Conpronises nust be
nade ia order not to sake the gane too conplicated or too tedious to pley. But without a
realistic baso & sinulation nodel has no raison d'etre since it is in learning through
sinulatioa' of real life situations that serious ganes have a useful role.

503

inte taction oi luJs CPifigrt*

As v« indicated earlier, oar experience supports the cosclusios that the serious gaae is do
better than any otkar aatkod for taacking about suck coacapts as tax base, rata of return,
davalopsant costs, ate. All these idaas could just as vail ba dafisad asd discussad in a for sal
classroos setting. However, vhas it cosas to illustrating tka intaractios of all tka aconosic,
political, and social forcas affecting tka private and public davalopsant of an urban araa and
rasulting in axisting citias vitk thair various problems, tka sarious gasa raprasasts a suparior
padagogical technique.

Perkaps an axaspla vill saka tkis point sora clearly. Aftar playing lav Tovn tka studants
vara quita capabla of discussing such questions as: Iky in a city ilka St. Louis is a larga
concentration of industry found between tka railroad station asd tka rivar? Iky do skopping
centers spring up? Uhy in citias tee thara larga coscaatrations of luxurious rental proparty
beside parks and lakas? How ara tka locations for parks, schools or otkar public davalopsants
determined? Hov do privata developers and the city goverasent interact to develop a city? To
ansver any of these questions one oust have an understanding of tka istaraction of the variety
of forces that are present in an urban environsent. With never versions of lav Tovn which
include ecological constraints, students can ba lad to consider suck additional issues as the
problass of building on a flood plain, the building of levees, and the affect of industrial
pollution on urban growth.

All these topics could certainly ba discussed in a formal classroos setting. However, it
would entail a great deal of lecturing to give enough basic inforsation to tka studants so that
they could begin to sea the interrelationships involved. Inforsation regarding these setters
and many otkar concepts and interrelationships can ba sada to fall out naturally fros tka
experience of playing a sarious gase. And, as was pointed out earlier, tka sarious gasa approach
is lass tedious as veil as sore fun for all tka participants than tka forsal lecture.

This is not to say that playing such a gasa as lav Tovn has tka sagical affect of saking
all the students experts in urban planning. Bather, the gasa presents to the studants in a sora
concentrated and sora palatable fors such of the basic inforsation necessary to begin an in-
depth study of the planning problass of a city.

1. Gase is available in both computerized and uncos puteri zed form fros: Harwell Associates,
Box 95, Convent Station, lev Jersey, 07961.

2. J. Shatftc and 0. Buss, &S4lU4ii2fl Si i.»*rning lfii latoceatlsa Ptillzatloo in &

Cosputer-Sisulated gcoqgpig JLg&ftl* Proceedings of the Second Annual Conference on Cos pu tars
in the Undergraduate Curricula, 1971, p. 94.

3. Developed by Alan Feldt of Cornell University and available fros: Canter for Housing and
Environsental Studies, I. Sibley Hall, Cornell University, Ithaca, lav Tork

BOTES AID 8BFBBEICES

504

POLITICAL SIMULATION AND THE MINI-COMPUTER
A CHALLENGE To THE INDUSTRY

Marshall H. Whithed
Teiple University
Philadelphia, Pa. 19122

Suanary

This article discusses the uses of computer-assisted political simulation models, and the
requirements such simulation models i mpose upon the computer system which is utilized. The
author suggests that the educational goals sought in the use of political simulation exercises
are best attained through the utilization of a conversational mode time share computer facility,
or, alternatively, a dedicated facility, on a conversational interactive basis, although a
number of computer problems are thereby created.

The authors work has not been with mini-computers, but rather, with large computers on a
time share basis. In terms of the present interest in mini-computers, the author discusses his
experiences in the large-computer time share world, with illustrations provided by means of a
number of urban simulation models he and his group have been working with in the past several
years. The requirements of the work are discussed in detail, from the user's viewpoint, as a
challenge to the mini-computer industry. The suggestion is made that a dedicated mini-computer
should be able to accomplish the requisite tasks, and maybe do this on a cost-competitive basis
when the true, rather than ideal, performance of large-scale time share computers is taken into
account.

Political Simulation

Political simulation may be regarded as an experimental technique through which complex
political phenomena such as a political campaign or an international relations crisis involving
a series of events and a number of nation-state "players" may be "recreated" under quasi-
experimental conditions at the will of the person conducting the simulation. As such, then,
simulation techniques have the advantage of controllability; that is, the circumstances may be
altered at will, and especially, the tiling of the exercise may be altered to suit the
convenience of the researcher or of the teacher.

Simulation techniques are not new, and in fact have been applied for a number of years in
the field of business management]] 1]. In political science, simulation techniques have been
previously applied to international relations and foreign policy situations. A particular case
in point is the Inter-Nation Simulation, which has been utilized extensively at Northwestern
University and several other universities. A teaching version of this model is marketed in kit
form by Science Research Associa tes[ 2 ]. In the field of American Government and Politics, there
is an election game developed by James S. Coleman which has been utilized at the Johns Hopkins
University and in the Baltimore high schools. A national political game has been utilized at
Kansas State Teachers College under the direction of Dale Garvey, and an American Government
game under Robert Alparin at the University of Maryland. A preliminary version of a presidential
election simulation prepared by Marvin tfeinbaum and Louis Gold, since published by Holt,
Rinehart, and Winston, has been utilized by this writer on an experimental basis in Basic
American Government classes at Northern Illinois University and Temple University.

dost of these simulation models are intended to teach the participants particular skills or
how to perforin particular functions, such as being the head of state of a country, devising
viable military strategies, or managing a large . business. A major inducement to the utilization
of simulation techniques in such situations is that the participant can learn from his mistakes
without suffering the real-life consequences when mistakes are made while learning. A
participant in a business management simulation may, through poorly conceived strategies,
bankrupt his company and learn from the experience without actually losing real world money. The
miscalculated foreign policy decisions of the head of a simulated state may lead to war and thus
provide the appropriate lesson for the decision-maker without incurring the social costs of
actual war. In short, simulation exercises are useful in teaching skills when the consequences
of error in the real life context are so costly as to effectively prohibit trial and error
lear ning[ 3 ]•

While these reasons are in themselves significant motivations towards the utilization of
simulation techniques, there are other advantages as well. In particular, many have long
recognized that the academic classroom is not an adequate setting in which to convey to students
an understanding of the complexities, inter-relationships, and dynamics of political phenomena,
or most complex social phenomena for that matter. Partially in reaction to this problem,
teaching political scientists have for some years been utilizing supplementary teaching

techniques such as pol
agencies. Unfortunately,
instructive positions a
campaign participation fo
students involved in a
such as licking stamps, a
do they find themselve
important campaign decisi
finds himself in a posi
and thus experience, the

itical compaign work
however, there is a de
vailable to college
r his students as part
political campaign are
nswering telephones, a
s in positions from
ons are made. And it
tion in the campaign o
decision-making proces

and in-service training in public administrative
finite limitation on the number of meaningfully
students. As anyone who has included political
of his course requirements is aware, otten
relegated to relatively un instr uct i ve activities
nd handing out the candidate's literature. Seldom
which they can observe the processes by which the
is a very infrequent occurrence when the student
rganization where he can actually participate in,
ses.

Arranging for public administration internship or equivalent experiences for students also
presents the problem of a liaited number of suitable openinys, as well as consuming a great deal
of professional time in developing and establishing the openings. And many of these openings
reguire a considerable amount of travel for the students between campus and job.

Given these circumstances simulations offer an attractive alternative which provide not
only a sufficiently large number of meaningful instructive positions, but ones in which the
participants can learn how and why decisions are made through actually functioning as a
decision-maker and by experiencing some of the cross- pressures and consequences of decision-
making.

In political scie
simulation models. Amon
Community Land Use Ga
time-share computer faci
focus on aul t i- na t iona
and a computer-assisted
experiences with these
computers in political s
pursuits.

nee curricula we have been experimenting with several computer-assisted
g these is an urban land use game, which we have derived fnm the
me (CLUG) originally developed by Allan Feldt[4]. He have developed for
lities, an international relations simulation model with an especial
1 business considerations, called Politically Simulated World (PSW)[5],
version of our Woodbury: A Political Campaign Siaulat ionf 6 1. From our
models, we have come to several conclusions regarding the role of
ioulation modeling, and particularly with reference to educational

Basical] y, ve found it necessary to move to the use of
mass of data inherent in anything more than a very simplistic ef
environment within a reasonable time span and with a reason
earlier efforts at batch-mode processing simulations, such as ou
(PS V) exercise, we found it necessary to resort to a cooputer to
in time for the next simulation period. In one of our early runs
were in fact running two separate games, a computer breakdown fo
do the calculations manually; this task took one of us, who i
nearly two full days of tedious effort to complete. Thi
discouraging in terms of everyday class use, and of course would
model in a continuous simulation run of many repetitive cycles.

computers in order
fort at modeling t
able effort input,
r Politically Sin
make the necessary
of the PS W simulat
reed the simulation
s an accomplished
s type of work 1
prohibit utiliza

to handle the
he oolitical
Even with our
ulated World
ca lculations
ion, when we
directors to
accountant ,
oad is rather
tion of the

Besides the procedural proble
found through extensive experience th
cannot feed the results of analysis
in the simulation cycle, but rather,
order to allow for batch input and ou
of view, batch-mode processing often
participants. This results in les
comprehensive feedback could be provi
participant interest which might ha
could have been provided.

ms inherent in a batch-mode Drocessin
at batch-mode computer processing of
to the simulation participants at the m
must introduce data at an artificial
tput procedures and handling. And from
precludes rapid and meaningful feedback
s learning than might be the case
ded at the moment of interest, and also
ve been sustained or even heightened if

g situation, we have
ten means that we
ost appropriate time
ly-delayed time in
an educational point
to the simulation
if more rapid and
perhaps a loss of
more rapid feedback

The desire for more timely introduction of data from the previous simulation round into the
next cycle, plus the desire to provide more rapid feedback to the simulation participants, have
led us to explore the time-share computer mode for teaching simulation work. Using a remote
computer terminal, a simulation operator is able to input the data resulting from participant
decisions in a particular simulation cycle and to receive back on his terminal within a matter
of minutes the new simulation data updated as a consequence of the previous participant
decisions.

Educationally-speaking, we find that the time-share approach not only provides much more
rapid feedback for the simulation participants, but also makes it possible to program the
simulation model so that participants can, using the remote computer terminal, explore the
potential effects of v trious alternate decision strategies open to them. In short, time-share
makes possible an int .ractive process between the simulation model and th.e participants.

Finally, it is perhaps worth noting that a carefully-constructed educational simulation

computer program can, with a well-laid out series
terminal, make the administration of a complex

of query statements
simulation exercise

through the remote
much easier tor the

499

506

simulation director. And anybody who has run a session of hand-controlled CLOG or another
similar simulation exercise can well appreciate this last.

In order to accomplish these objectives, and especially the last, it is necessary that the
computer program "ask" the relevant decision- point questions at the appropriate point in the
simulation cycle. Furthermore, these queries must be made in a clear manner easily
understandable to the user of the simulation model (rather than being structured according to
the computer technician's point of view), and the response patterns should be clearly apparent
to the user. In short, we here envision a conversational mode of man-computer interaction via
remote computer terminal, and this is only possible through the time-share environment.

In the paper we discuss our experiences in developing a computer-assisted version of the
Woodbury Political Campaign 5i,au}at ion, including an analysis of the educational motivations
which led us to perceive the necessity of a time-share environment and conversational approach.
Next, ve examine an urban land use simulation model, CLUG, in its human-controlled and early-
version batch-mode computer-controlled version for the IBM 1180 as developed at Cornell
University. In particular, we find that with either the human-control or batch-mode computer
approaches, the necessity of emphasizing accounting and preparation of specific format inputs on
punchcards distracts greatly from the simulation participants' abilities to concentrate on the
substantive aspects of land use development because they must of necessity spend too much of
their time on the mechanics of filling out paper forms or punching specific format Hollerith
cards. We therefore have developed a time-share version of a modified CLUG model, in which the
conversational "abilities" of the time-share approach rectify this problem, and also make the
exercise much easier for a simulation director to administer.

Pinally, the possibilities of using mini-computers to fulfill the same educational
objectives that led us to use time-share facilities are analyzed and discussed.

Urbayi Electoral Simulation Exercises

In the urban context, a number of urban land use development and urban electoral simulation
models have been developed, including the ones ve report on here. Some of these models have
become quite intricate, and embody the land use developmental, political, social, and economic
sectors of the urban polity. Some of these models have been used tor teaching and, tentatively,
to explore with urban decision-makers some of the outcomes of various alternative strategies of
action open to them.

The Woodbury urban mayoralty election simulation is a simulation of urban-oriented
political interactions. As played thus far, with an exception to be noted later, it has been a
"man simulation," that is to say, human actorn play various roles, and the scoring is performed
by human umpires. The scenario for the exercise portrays a hypothetical community, is
constructed for teaching purposes, and so contains a considerable number of urban problems for
the simulation director to explore with his students.

The participants occupy various campaign roles, such as the mayoral candidate's
organization, pressure groups, the mass media, and so forth. Their actions ace constrained by
the parameters contained in the scenario documents, and as the simulation exercise unfolds, new
parameters upon their actions are established by the activities of the other role-playing
groups.

The 'pay-off' mechanism for the role-playing groups is a two-fold one. The first level of
payoff is the simulation election for mayor, for obviously one candidate wins and the other
loses. This function is performed by the umpires as described below. The second level of
payoff, centering upon the various pressure groups, is generated by the simulation participants
themselves in their peer group interactions. Each pressure group formulates a goals list and a
strategy to achieve those goals through gaining the assistance of other groups, and ultimately,
the support of one or both mayoralty candidates for their position.

Basic to the man-simulation model of the Woodbury simulation is the function of umpire.
Woodbury is divided into nine wards (ten wards in a special ten-ward model), and an umpire is
assigned to each ward. In our runs of this simulation exercise, the umpires have been graduate
students and professors of political science. Probably a group of umpires could also be
recruited from knowledgeable townspeople, politicians, and civic groups. The umpires assess the
various moves of the roleplaying groups, moving prospective votes from one candidate to another
and/or to or from the politically independent column. The roleplayers generate numerous moves
during a simulation run**- some Woodbur v games have generated more than 200 moves to be assessed.

The utilization of human umpires who are particularly knowledgeable about the subject
matter to do the scoring and thus control the outcome of the simulation exercise is similar to
the use of experts in the field of international relations and diplomacy to judge the direction

507

•:? >? >

500

of an international relations political siaulation exercise, the Political M
PM E[ 7 ].

In our exprrienc
■odel has a number of a
necessity of numerous
a city to be simulated
approach more or les
other variables. And to
scientists for the simp

e, the Ban-uBpire approach to the Woodbur.y-t y pe urban
dvantages, particularly for teaching purposes. But on
ward umpires poses a serious logistical problem as th
is increased. Also, the logistical coordination burde
r. effectively preclude much extension of the Bodel
r regular teaching purposes, the necessity of find
lier Woodbury- type model Bay pose problems at smaller

il ita

ry Ex

erci

se or

poli

tics

SiBU

lation

the

ot her

han

d , the

e nun

ber o

f tfa

rds in

ns in

the

Ban-

uBpire

to ta

ke into a

ccount

ing

nine

political

colleges.

For these reasons, we have developed a computer-assisted version, and have utilized the
model in the classroom[ 8 ]. In the computerized version of the Woodbury model, the Various groups
in each ward are treated as "Voting Block Reaction Groups.” As in the original man simulation
model, student role-playing groups initiate moves or political actions. The simulation director
codes the verbally-expressed moves into a preestablished coding scheme in the sane Banner as
open-ended survey questionnaire responses are coded into numeric format for computer analysis.
When inputed to the computer according to the predetermined coding scheme, these aoves are
"evaluated" in terms ot their specific and cummulative effects upon the VBR Groups of each ward.
From the data base stored in the computer program, the reaction weightings for the VBR Groups in
each ward are generated on a *9 scale. Vote distribution shifts of potential voters are
reflected in the "Gallup Polls" provided to the student participants through the remote computer
terminal as indicators of the success or failure of their strategies. The vote distribution
shifts are totaled for each Gallup Poll, and at the conclusion of the simulation exercise the
computer translates the potential voter data of the Gallup Poll into "Actual Vote" totals for
each ward, according to preestablished formulas representing the differential between potential
voters who would be tapped in a political survey (Gallup Poll) and the actual voter turnout at
the polls (as expressed in the voting behavior model for the simulated city, upon which the
computer weightings and formulas are based).

The computer printout provided to the participants during the simulation exercise is
designed to provide role-playing teams with detailed information regarding the political effects
of their specific political moves. Because of the rapid interaction between the role-playing
team participants and the simulation model through interactive con versa tional mode time-share
computer terminals, quick feedback can be provided to the participants. Additionally, role-
playing groups can utilize the remote terminals to explore the effects of VBR Groups of various
alternative strategies before committing theii group to a particular strategy.

Although the focus of this article is on educational usages, some of the facets of the
urban electoral simulation model we are here describing would also be of obvious value to
political planners. In fact, work has for some time been underway on a generalized urban
electoral simulation model, called General Urban Election Simulation System (or GUESS), of which
the computerized Woodbury simulation is a specific variant. In GUESS, urban electoral data
specific to a particular city will constitute input to the general GUESS program.

In an article to be published elsewhere, I suggest that politicians, or public affairs
decision-makers generally, have for different reasons much the same needs of rapid nd
conversational mode interactive feedback in simulation planning models as the educator.

At the heart of the computerized Woodbury simulation is the necessity of a time-share
computer system which is reliable. Given the present state of the art, the reliability criteria
implies having the program mounted on a back-up computer system. Unlike an all-computer
siaulation, mixed man-machine simulation systems such as the computerized Woodbury model involve
a sizeable grouping of human participants who must have appropriate feedback at the requisite
time in the simulation cycle, and significant delays in providing that feedback often distorts
or destroys the model and/or the group dynamic which is a part of these exercises. In fact, it
may well be that social scientists in the simulation field make more sophisticated demands on
computer hardware than their "hard science" colleagues, because of their need for dependability
of servire. Additionally, the social scientist often works with sizeable collections of data,
raising questions of computer core capacity and/or procedures to store data economically on tape
and providing access to the tapes when required (at least one major computer time-share company
we have worked with abhors hanging tapes, and the writer can testify from his experiences at
several academic institutions that university computer centers are often reluctant to do so
also. )

The challenges from the computer point of
of reliability (it's hard to tell some fifty sia
later; the computer's died again," or "you'll
fix the computer," and keep things rolling), inp
sharing, conversational interactive modes, th
computer responses in a English language format
understand as possible) , and computer stora

view, then, seem to be associated with questions
ulation participants to "go home and come back
have to wait for your budget reports until they
ut and output routines (for our purposes, tiae-
at is to say, computer queries for input, and
as easy for the user ot the simulation Bodel to
ge capabilities (either large capacity core and

501

508

disk/drum, as the UNIVAC 1108 or General Electric Hark II Tine Share system, or peripheral and
cheaper storage of the bulk of data on disk or tapev provided that the computer installation is
willing to hang tapes to run a program with, let's say, at lost five or ten minutes lead tile,
and that the computer system response as it appears to the user a£. the remote terminal , once the
tapes are hung and the program under way, does not exceed, let's say, thirty seconds* in our
experience with a cooperative computer center, these criteria imply that tape storage can be
used in political simulation modeling- And/or, chaining of the program (s) may be undertaken, as
is being explored with some of our simulation programs presently- Utilization of these
techniques may well also open up this market to the mini-computer.

U£ba n Land Use Simulation Models

Several simulation models have been developed to explore alternative patterns of urban land
use development- One of the earliest of these models, a fairly simple one useful for
instructional purposes, is the aforementioned Community Land Use Game (CLUG) developed by Alan
Feldt and associates at Cornell University.

The basic CLUG exercise is based on a grid-marked playing board, "playing pieces" to
represent various types of urban construction (residential, industrial, commercial, etc-), and a
player's manual describing the sequence of play in each round and other rules, and cost data tor
each type of conci tr uct ion, transportation costs, and so forth. Three teams, of several players
each, represent both private entreprenurial and collective community functions; representing the
private sector of ihe economy, they seek to maximize their financial return by careful planning
of their investments, and in their community role the teams must decide, by majority vote, upon
the extension of so-called "utility segments" (representing functions such as police, fire,
water, sewerage, and other such municipal services) to various parcels of land before private
interests may build on them and realize profits. The utility segments, costing stated amounts to
construct and to maintain each succeeding round, must be paid for out of community funds derived
from the agreed-upon tax levies.

The model provides for variable land assessment patterns, to reflect changing land values
brought about by development of surrounding parcels of land. A mechanism is provided to take
into account depreciation in building values over time and a simple probability routine, which
takes into account maintenance standards of various owners, is utilized to simulate the
possibilities of loss of building use through fire, vandalism, or some other natural calamity.
Transportation costs, varying according to type of material to be transported and class of
roadway to be used, are calculated and charged to the appropriate team*

The simulation model is in actuality rather simple, although guite useful for instructional
pruposes, and it does produce "constr ucted" cities quite similar in appearance to many real-
world cities. In any event, it does not come close to the complexity of the other available
urban development models, such as METROPOLIS or REGION or CITY. Even so, however, to make the
necessary calculations by hand for each round, and to record the necessary data for use in
making following rounds' calculations, is a quite tedious job as anyone who has run CLUG for
many successive rounds can testify. Additionally, ve often find that the players are more pre-
occupied with their complicated bookkeeping than with the facets of urban development we are
concerned with teaching.

An additional problem is that it is not feasible, using hand calculation methods, to
increase the complexity of CLUG much beyond its early status* Although we have added two more
teams, and made a few other alterations in our work with CLUG, not much extension is possible
because of the logistical problems*

pur

dat

res

far

Under these circumstance
perform the requisite calcul
Cornell University; it i
poses, however, it requires
a cards, and also does
ultant printout does not con
developed*

s, it seemed reasonable to consider developing a computer program
ations. And indeed, a computer program has already been developed
s a batch-mode operation for the IBM 1 130. Unf ort una tely for our
much attention for specific formating on the keypunched input
not perform all the necessary calcula tions. Additionally, the
tain all the relevant data about the simulated community as thus

In short, two major flaws with the existent batch-mode program emerged
the man-controlled mode of simulation play, the participants would be spending
attention t.o questions of data format, at the expense of concentration on the
land use, and (2) the computer output was incomplete.

(1) again, as in
too much time and
dynamics of urban

This being the case, it
computer program in a time-share,
available to us. The program
land, construction of facilities
appropriate to the simulation

was determined to start anew, and to develop an appropriate
conversational mode environment since these facilities were
as now developed "asks" questions for player decisions (buying
thereon, utility extensions, etc*) in the correct order as
model. The questions are typed out in English ou the teletype

509

v . * >r '

50Sl

unit, along with instructions for
flows and the new cash reserves
the land use configuration of the

user response. The program calculates the appropriate cash
for each teai. A nap is also printed out each round, detailing
sinulated connunity as thus far devel oped[ 9 ].

runn
nod i
pro v
wor k

Me find th
ing sessions
fications in
ides us with
with Dili's pr

at the existence of the tine-share conputer program considerably assists in
of a CLUG-type simulation (as we constructed the program, we nade a nunber of
the sinulation nodel at the sane tine). Additionally, the conputer vehicle now
the option of adding various subroutines to the sinulation nodel in our further
o ject.

Pron the point of view of conputer technology, the criteria I raised earlier in this paper
when discussing the urban electoral nodels pertain. Criteria of dependability, input ard storage
of large amounts of data, and conversational tine-share nodes predominate.

Computer Requirements For Political Sinulation Modeling

our approach t political sinulation modeling to date has emphasized the use of large-scale
time-share computing because that is what was available to us. There have been a nunber of
problems in this approach, however. The problems usually center around the fact that nany tine-
share computers do not at all live up to their billing in terms of response, time, and
especially in terms of dependability. In part this may be an artifact of our doing most of our
work at academic computer centers, and with one or two possible exceptions I have yet t> see a
university conputer center which meets the criteria established in the preceding pages. And at
least one of the major computer time-share conpanies in the commercial marketplace is
customarily characterized by very slow (over several minutes) response time in the middle
afternoons when demand on the system builds up.

Given the near unusability of many time-share computers for effective political sinulation
modeling, a recalculation of costs and benefits for the large-scale time-share conputer and the
mini-computer may be in order. For the typical cost comparisons seem to be based on the
assumption that the larger machine docs in fact what it is supposed to do. But given the
realities of large machine performance, especially in the academic world, it may be that the
cost comparisons do not in fact favor the larger machine..

The cost in programmer time, as well as computer time, lost in "bombed" runs on an ailing
time-share system can be considerable (For one simulation class I know of, the professor ran up
several thousand dollars worth of computer charges on his department at one university in
attempting to mount his programs, finally gave it up as a complete loss, ^and vent on during the
next semester to refuse to teach the class at his home institution and to accept a part-time
faculty position at a neighboring institution and teach the same course there— using that
university's computer center.) Faculty members at more than one school have been known to leave
for another university where computer service was better. And a recent Hand Corporation report
on the efficiency and effectiveness of university computer centers suggests the efficiency
situation with many academic computer centers is somewhat less than rosy.

Given the fact that the social sciences are increasingly coming to recognize the i ance
of computer analysis, and given the difficulty social scientists have in accoaplishi their
work with the large-scale computer at the university computer center, social scientists at a
number of universities occasionally give thought to the possibility of acquiring sa computer of
their own, perhaps shared between several social science disciplines, and under ^heir control.
At least, so the thinking goes, perhaps some of the smaller projects could be put on "our own"
computer, and the large jobs left up to the "number cruncher" at the university computer center.

The Mini-Computer To The Rescue?

Such thoughts have come to my mind a number of times when we have been having some of our
more colorfully-exasperating sessions with the computer center, and so the opportunity to
analyze these possibilities as a form of challenge to the industry in this article was welcomed.
Given this opportunity, we have given some thought to the real nature of our requirements, and
given that, to the ways our programs might perhaps be modified to accomodate the context of the
mini-computer environment and also accomplish our goals.

First of all, we will
consequently its small cost.
That being the case, we will
This will accomplish, for our

assume
it wi 11
assume t
purposes

that, given the small size of the
be "controlled" by a relatively small
hat can dedicate its total use during
, the sane effect as time share.

mini-computer and
number of users,
a simulation run.

data

does

The machine's typewriter unit, or perhaps an attached teletype, can be utilized to input
and commands, and to receive the results back, as the teletype unit on a time-share system

503

510

Obviously the major problem centers upon computer core storage capabilities. Here, sole
ingenuity is in order.

The present version of our TeleCLUG urban land use simulation game prograa takes soae J2K
of core on a UNIVAC 1100 for tile share. While it is true that the present prograa is "sloppy"
and "cleaning up” will shorten it considerably, we are still talking about something
considerably larger than oost a ini-compu te r core sizes.

However, "chaining” of programs aay enable an apparently larger program to be shoehorned
into a smaller core. The Tele CLUG program, for example, was designed to be chained for a
smaller coaputer, although that is not necessary for the present version on the UNIVAC 1108.

Also, the reader will recall that in earlier sections of this article I suggested that a
response time of upwards of thirty seconds, or maybe even a little more, would not be a
significant impediment to the work at hand. Considering that a good tine share system talks
about a response time of well under a second, this latitude should provide plenty of room to
work in. In particular, with a dedicated machine, the use of disk storage, and perhaps some
resort to tape (as, for example, the extensive 1 data files in the Woodbury urban election
simulation, as was done when that simulation was on the General Electric Time Share service) may
prove to be a usable solution. In Particular, if upwards of a thirty second response ot the
total machinery to the user is tolerated, considerable with in- program disk referencing might be
possible.

All of this may not seem "efcicient" in terms of cost comparison with larger machines in
the ideal sense, but when the fallacies of the larger machinery are taken into account, the
dollar costs, as well as frustration aspects, may well rebound to the benefit of the mini-
computer.

FOOTNOTES

1. Perhaps the leading example is the IBB Hanagement Decision-Baking Laboratory. See IgH

Banagement Decision-flak ing Laboratory ; Institute for Partici pa n ts , and the companion.
Admin ist ra tor *~s ^Reference Ha nua 1. IBH, Technical Publications Department, 112 East Post
Road, Whie plains. New York, 1963.

2. Science Research Associates, 259 East Erie St., Chicago, Illinois. Researchers at

Northwestern University are working with a computer-controlled variant of the INS, called
the International Processes Simulation. Several faculty members at Rensselaer Polytechnic
Institute and Northern Illinois University are working on the development of a multi-
national political, economic, decision-making simulation called PSV-1# This simulation,
which is computer-controlled, provided for the generation of machine readable records of
role-player decisions for subsequent analysis. (See John Parker, Clifford Smith and
Marshall tfhithed, "Political Simulation: An Introduction" in H. Ned Seelys, ed.. Handbook
for Teaching Latin American Cultural Themes, Illinois Department ot Public Instruction,
Springfield, Illinois, 1965, Ch. 5).

3. Colonel William Thane Hinor, Director of the Simulation and Coaputer Directorate of the

Industrial College of the Armed Forces in Washington has suggested in this regard that:

"Economy of time, risk, manpower and dollars are key factors which make simulation useful.
In the real world, it aay be costly, or even impossible, to wait tor feedback resulting
from required decisions or for the results from suggested contingencies or selectable
alternatives ... Decreasing risk, particularly where safety of people and property is
concerned, has been a function of simulation for many years ... The economy of manpower is
apparent in simulations where one individual may represent a group, an organization, or a
political entity or where a small group of individuals may represent an entire nation ...
(Finally) simulations which describe the ’state*; or changing ’states* of rea 1 it y--usually
cost fewer dollars than programs operating within reality for the same purpose." See Col.
William Thane Rinor, "Current and Future Uses of Time-Sharing in Educational Simulation,"
Simulation and Computer Directorate, Industrial College of the Armed Forces, Port Lesley J.
McNair, Washington, D. C., October 1968, pp. 4-5.

4. Allan G. Feldt, The Comm un itx Land Use Game, The Center tor Housing and Environmental

Studies Division of Urban Studies, Cornell University, Ithaca, M. Y., 1966.

5. The authors of the PSW Simulation are John R. Parker of IBH, Clifford N. Smith of Northern

Illinois University, and Marshall N. Whithed. The model is discussed in Parker, Smith, and
Whithed, "Political Simulation: An Introduction," in H. Ned Seelys, ed. , Ha ndbook for

Teaching Latin American Cult ura 1 Themes, Illinois Department of Public Instruction,
Springfield, Illinois, 1968, Ch. 5. The simulation is programmed in PL/1 tor the IBH
360/40, batch-mode processing.

511

Sffl'l

A manual ly-cont rol led (human umpire) version of this simula4ion model is to be published by
Litt le , brown and Coapany. The authors are ri. Roberts Coward, Bradbury Soasholes, and
Marshall Whithed- It deals with an urban mayoralty election campaign.

The Political nilitary Exercise was first developed by Goldhamer et- al. at the BAND
Corporation; see H. Goldhaaer and H. Speier, *'Soio Observations on Political Gating, "Wo£ld
£2lkii£§# Vox. XII, October 1959, pp. 71-03. See also H. Roberts Coward, The Political
fliiiim as a le^SL&ilU Device in EoiiU£4i Science; 4 Handbook, final Report,
Project No, 6-0964, Contract No, OEC-3-7-Q6H964-;n 99, U. S. Department ot Health,
Education and Welfare, Office or! Education, Bureau of Research, Washington, D. C. , 1969,

Credit for Baking the devel opre ntal work possible oust be extended to the General Electric
Coapany, which provided the computer tiae and facilities for development of the prototype
program- Mr. Robert Lund who, as senior programmer, devoted auch "midnight oil" to the
project, Mr- Lawrence Birch who served as research assistant, and Mrs- Cherie Caapbell who
assisted in developing the statistical format for the simulation model- Hr- Kirk Sorensen
adapted the program to the UNIVAC 1100, which was used in the classrooa exercise.
Rensselaer Polytechnic Institute provided a Faculty Research Grant tor carrying out some ot
the necessary work on the original development of the coapu tor-assist ed model.

The program, presently undergoing modification, was developed by fir. Kirk Sorensen of
Rensselaer Polytechnic Institute in the spring of 1970 and used in a class for the first
time in Hay of that ye«»r at State University of New York College at Plattsburg. It is
programmed in FORTRAN on the UNIVAC 1100, and is designed to be adaptable to other
machines- Credit and thanks is due to the staff of the Computer Center ot the State
University of New York at Albany, which provided the computer facilities for this
developaent. The land use map in this program is, as far as we know, the first one
available over a teletype for this family of instructional urban land use models- Other
models, such as CITY, provide a land use map, but only over a regular printer, and so the
output must be carried from the coaputer site to the simulation room-

505

THEORY OP PROBABILITY AID STATISTICS
ILLUSTRATED BY THE COMPUTER

Elliot A. Tints
Hope College
Holland, Michigan 49423
Telephone: (616) 392-5111

Background

During the past few years several Hope College seniors have done research projects in
probability and statistics using oar IBB 1130 coaputer. These projects often reguired coipater
simulation of either a physical experisent or a probability distribution. It becaae increasingly
clear; that in order for a student to write a coaputer program that would properly perform the
simulation, the student had to understand the theory of the problea and the student also gained
a greater appreciation for this theory.

It was then suggested that all students taking our two seaester junior-senior level
mathematical probability and statistics course should have this opportunity of increasing their
understanding and appreciation of the theory by performing simulations on the computer. A
drawback to this approach is the class tiae reguired and also the extra tiae required by a
student outside of the classroom. It was also obvious that additional preparation tiae is
required of the instructor of this type of approach.

It became clear that the addition of a two hour laboratory each week would provide tho
additional cliss tine. In order to prepare materials for th» laboratory and to provide
additional preparation tiae for the instructor, it was decided to subnit a proposal to the
National Science Foundation. This proposal was funded. The grant froa HSF is not only permitting
us to develop aaterials for this laboratory, we are also developing materials for an
introductory statistics course taught by Professor Herbert Dershea in which statistics and
computer programming are interveaved in such a way that the student always has learned enough
programming to program the next statistical technique and knows enough statistics so that the
latest programming principle learned can be illustrated .by exaaples Involving .previously learned
statistics.

During the susaer of 1971 we developed software and wrote many of the laboratory exercises.
He were assisted by four of our mathematics majors who had taken both the mathematical
statistics course and the computer programming course.

During che 1971-72 academic year we are introducing the laboratory for the first tiae to a
class of 24 students. An outline of the laboratories for the first sc^aest^r is given in Section
3.

During the susaer of 1972 we plan to develop additional software, revise our experiments
and design soae new experiments. He shall also be holding a one week conference in August for
about 50 educators froa the Midwest who are interested in these programs.

Following the 1972-73 academic year, during which the revised laboratory materials will be
used with another class of students, ve shall evaluate the entire project and sake
recommendations for the future. Hopefully ve will be able to dist. ibute aaterials during the
suaaer of 1973 that have vide applicability.

klkaiator* Des££iEtion

The laboratory is used to show that certain physical experiaents do satisfy particular
probability properties. Sone of these experiaents are then simulated by the coaputer. An
additional key purpose of the laboratory is for the student to understand and appreciate the
theory of probability and statistics by writing coaputer programs. Thus vr< assume that our
students have taken computer programming. Re do provide a randoa lumber generator, various
plotting subroutines, and additional subroutines when needed.

The following listing gives the topics covered in each of the 15 laboratories during the
first seaester. In Section 4 ve shall describe two experiaents.

Description

Laboratory

Topics

Relation between a balanced spinner with a scale froa 0
to 1 and a computer pseudo-randon number generator.

513

Probability as relative frequoncy - flipping a coin, a
pair of coins or rolling a die - first dona physically
and than siaulated using tha pseudo-rand oa nuaber
generator*

2 Parautations and coabinations, hypargaoaetric
probabilities* (Subroutines for drawing balls froa urns
and cards froa a deck of playing cards were used*)

3 Expectation*

4 Conditional probability, Bayes9 foraula, independent
events.

5 Bernoulli, binoaial, negative binonial, and geoaetrid
distributions*

6 Eapirical distribution for a single vari; ole: histograas,
ogives, eapirical distribution function*

7 Relation between probability density function and

relative frequency histograa for the binonial and

geoaetric Attributions*

8 Coaparing the theoretical and eapirical aean and

variance for each of the binonial, hypergeoaetric,
geoaetric, and negative binoaial distributions.

9 Poisson distribution*

10 Eapirical distribution for paired data*

11 Hultivariate, aarginal, and conditional distributions

for discrete randon variables*

12 Randon nuaber generators, distribution of ll = o ♦ V
where 0 and ? are independent unifora randon variables,
distribution of l * G(H) where G (w) is the distribution
function of V*

13 Hultivariate, aarginal, and conditional distributions

for continuous randon variables*

14 Generate randon saaples froa the exponential, gaaaa,

noraal, and chi-square distributions*

15 Generate randon saaples froa the bivariate noraal

distribution*

Soae of the topics which will be included in the laboratories second seaester are the
central Liait Theorea, noraal approxiaations, estimation, confidence intervals, power function,
tests of hypotheses, analysis of variance, chi-square and Kolaogorov~Sairnov goodness of fit
tests, and the sign test*

fil&UUs

He shall give a brief description of parts of two laboratories*

lafepyatgcy 9: le shall describe an experiaent for which the outcoae has a Poisson
distribution* He shall then show how the binoaial distribution can be used to sin*jlate a randon
saaple froa the Poisson distribution*

He often read in textbooks that if X denotes the nuaber of alpha particles eaitted by a
radioactive substance that enters a prescribed region during a prescribed period of tiae, then X
has a Poisson distribution* Hith assistance froa the Hope College Physics Departaent; we took
100 *1 second observations of the nuaber of eaissions by BA 133 using a geiger counter in a
fixed position* The students wrote a prograa to finJ the saaple aean and the saaple variance,
shewing that for the Poisson distribution these are about equal* These data are listed ia Table
1* To visually coapars the fit of the Poisson distribution to these data, a relative frequency
histograa was plotted along with the probability density function for' the Poisson distribution
with a aean of X * 5.61, the average of the 100 observations* This histograa is given in Figure

507

514

!• The subroutine that plots this histogran was written daring the Banner of 1*71 by one of our
students working on this project*

100 *1 SECOND OBSERVATIONS OF 8A 133.

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12.

11.

10.

6 .

Z .

5 -

8 .

3 •

10.

THE

SAMPLE

MEAN AND

sample

VARIANCE

ARE

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TABLE 1

To siaulate this eiperinent we used the fact that for large n and snail p binonial
probabilities can be approxinated by Poisson probabilities* Earlier in the course students had
learned to siaulate randon sanplns fron binonial distributions. For this exanple we used the
binonial distribution with n * 100 and p « 0.0561. Thus np * 5.61, the nean of the 100
observations in Table 1. ft randon saaple of sire 100 fron this binonial distribution is given in
Table 2. K relative frequency histogran of these data along with the probability density
function for the Poisson distribution with a nean of l * 5*61 is given in Figure 2*

A RANDOM SAMPLE FROM A 8(100,0.0561) DISTRIBUTION.

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11.

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SAMPLE MEAN

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ARE

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6 •
6.
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TABUS 2

508

515

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517

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L* bo^ajt 0£y J 4 : tfe shall describe a part of this laboratory that involves t l*e exponential and
ganna distributions.

is the distribution function of an exponentially distributed randoa variable with a nean of 9 *
1/2. The students are asked to sinulate a randoa staple of size 500 froa this distribution. They
know that if T has a unifora distribution on the interval (0,1), then X «F~1(Y) has an
exponential distribution with a aeon of 0 * 1/2.

Thus to enpirically illustrate this theoretical fact, a staple of 500 randoa aunbers is
generated, say Y 1^2' • * • 'Y500* For each Yi'xi * F ’<Yi) “ -<1/2)ln(l - y^) . A relative
frequency histogran for such a set, Xf,X2,.. ,X5qq, is plotted in Figure 3 along with the
probability density function f(x) = 2e~*x.\

Nov let **v2 '• • • 'V* be a randoa sanple of size 5 froa an exponential distribution with a
nean of 0 = 1/2. The students know that W « V1 + V? + ... + V5 has a ganna distribution with
paraneters 0 * 1/2 and - 5. That is, the probability density function of V is

zero elsevhere.

The students are asked to illustrate this theoretical fact. The sub of each consecutive set
of 5 nunbers in the sanple of size 500 generated froa the exponential distribution vas found,
yielding 100 v9s. A relative frequency histogran of these 100 v’s along with the probability
density function g(v) is plotted in Figure 4.

The reaction of students to the laboratory at this point is varied. One student said that
he appreciated the lab because he realized that in order to write a prograa he had to really
understand the theory. Students who had difficulty with progranning vere often frustrated by
error statenents which clouded their visioi. of the probability theory that vas being
illustrated*

In the first laboratories either too nuch aaterial vas covered or too nany exercises vere
assigned* It becane clear that it is better to illustrate less of the theory with three or four
veil conceived exercises. In this way the student has enough tine so that nany frustrations are
avoided.

This laboratory would not have been possible without the previous suaaer for preparation,
the released tine for ne during this acadenic year, and the student help in writing subroutines.
Ve are grateful to NS F for providing this opportunity.

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FIGURE

PSYSTAT - A TEACHING AID P01 I NTRODUCTOtY STATISTICS

Hare S. Weiss

Hashington State University
Pullman, Hashiogtoo 99163
Telephone: (509) 335-9915

Papers presented at «■ ho previous two conferences (e.g. Koh, 1970; Hikoff, 1970; Sandusky,
et al, 1971) have described the problems associated with traditional approaches to teaching
introductory statistics to behavioral and social science undergraduate majors. The use of a
computer statistics laboratory is an atteapt to resolve these difficulties which aay be briefly
restated as follows:

1. Students have weak (if any) real skills for handling quantitatively orieuted aaterial
and often have feelings of "dread" when they enter such a course.

2. Traditional enphasis on hand and desk calculator computations and computational
formulae often results in neglect of theoretical and conceptual material.

3. Absence of any meaningful laboratory experiments or demonstrations haudicaps the
development of an "intuitive" feel for basic statistical theory.

In addition to these problems, I was faced with two additional ones when confronted with
the prospect of teaching the psychology department's introductory statistics course. (1) The
lack of an appropriate text for a computer-oriented course and (2) the lack of appropriate
software easily i mplementable at the HSU computing center. Consequently , I undertook the
development of a software package (PSYSTAT) with the following goals in mind:

The package should be sufficiently general purpose so that it could be used with any
suitable standard text book.

2. The package should be easily transportable (written in FORTRAN) and modular in design
to allow for easy modifications and expansion.

3. It should be easy to use, require minimal learning effort on the part of the student
(e.g. formatting of input should be consistent regardless of options selected) and
should require no programming effort on the part of the student.

4. The programs should incorporate extensive diagnostics to catch student errors.

Since the HSU psychology department has no remote facility, the PSYSTAT package was designed to
be used in a batch processing environment.

Description of Course

The introductory statistics course in the HSU psychology department is a sophomore- junior
level course taken mostly by psychology majors. However, approximately 30* of the students are
non-majors. There are no prerequisites other than high school algebra. The course content is
traditionally devoted to both descriptive and inferential statistics. The topics covered when
PSYSTAT was used included frequency distributions, descriptive statistics using grouped and
ungrouped data, basic probability, the normal distribution, sampling distributions, central
limit theorem, parameter estimating and confidence intervals, t-test, correlation, introductory
experimental design and some distribution-free statistics.

Hhat follows is a description of the course given to students on the first day of class and
outlines the basic course philosophy and organization:

ELEMENTARY STATISTICS - INTRODUCTION
"The Purpose of Computing is Insight not Numbers" - H. H. Hamming, 1962

This could well be rephrased "The purpose of statistics is insight not numbers. " This
course is designed with this goal in mind. Statistical insight comes with practice and
experience and inevitably involves computation. Unfortunately, the beginning student often gets
lost in a naze of arithmetical computation and manipulation. Formulas and desk calculators pro-
vide little time for the development of insightful understanding.

Modern technology has provided a tool in the form of the high speed digital computer which
not only can eliminate the need for hours of hand calculation but also opens up a whole new
field of computer simulation. It is through this latter use of the computer as a tool for
experimentation that the hoped for insights will be developed. No programming skills are needed

521

514

and none will be taught. The student will complete two types of assignments: (1) hand worked

("paper and pencil") problems, and (2) computer worked ("machine") problems.

The paper and pencil problems are designed to familiarize the student with simple
applications of basic statistical concepts and theory. The machine problems are designed to
enable the student to perform "experiments" and compare results with the statistical theory. In
order to complete the paper and pencil problems* a student must:

1. Know how to write on paper with a pencil (or pen). 1

2. Know simple arithmetic.

3. Learn some statistics.

4. Be.able to think.

In order to complete the machine problems* a student must:

1. Learn how to write on "IBN" cards with a keypunch.

2. Read some simple instructions.

3. Learn some statistics.

4. Be able to think.

The point of all this is that "using the computer" should frighten no one. All students
will receive instruction in keypunch operation. A handout supplement will also describe use of
the keypunch.

Classroom dittoed supplements will be made available periodically* describing those aspects
of the course not covered by the text. There are no exams in the course. Bach Tuesday students
will receive an assignment to be completed and returned the following Tuesday. No late
assignments will be accepted. Each assignment will have a maximum point value. A students final
grade will ne determined by the total points he or she has accumulated. The grading system will
be discussed in class* but in general will be based on the individual score, not the

distribution of scores (if you don't understand this last sentence, read it again in two weeks).

Description of PS YST AT

The PSYSTAT package was developed not only to meet the challenge of improving statistics
instruction but to make a student's first contact with the computer a minimally traumatic
experience. To meet these goals the following features are incorporated in the package:

Input Data - these may be student supplied (all data unformatted with one datum per
car 37 or generated by the student via simulated sampling from one of four (or more)
populations. The populations available initially were the normal* biuomial* uniform*
and one called WEIRD which was asymmetric and bimodal.

Control Cards - a minimum of PSYSTAT control card information is required. The
following three cards are always needed: an Identification Card which labels the
output with the student's name and any other information he wishes to supply; a
Program Name Card which controls which of the 4 basic programs (DESCRIBE* T-TEST*
CORRELATION, STATISTICS) the student wishes to use; a Data Card which identifies the
source of data as being cards or a machine simulation.

Basic Programs - (These four basic programs are being currently supplemented with
programs to do simple analysis of variance* chi-square and non- para metric
statistics) •

DESCRIBE: The basic descriptive statistics program. Input is either grouped or

ungrouped data. Output contains a frequency histogram* a table of intervals*
frequencies and cumulative frequencies as well as a table of summary statistics
(mean* median* standard deviation* range* quartiles* etc.)

STATIST ICS: Can be used with any other program (or alone) and generates summary
statistics for input data.

T-T$ST: Performs one of three t-tests depending on input information. The output

contains sample size* degrees of freedom and the resulting t statistic.

CQRRELATIQN: Performs simple linear regression. Output contains the sample size*

correlation coefficient, two regression equations with standard errors for each of
the coefficients.

515

522

Error Diagnostics - Extensive error detection and error information capability has
been built into the PSYSTAT package* This enables the student (and instructor) to
diagnose the cause of an abnoraal program termination* As a result of my experience
this past semester, this feature is being expanded even further*

Sample Problems

Belov are two problems, one from the first (descriptive) part of the course and the other
from the later (inferential) part of the course* It should be noted that the basic simulation
for the first problem reguires a total of 5 cards or lines of input and 6 cards or lines for the
second* other sample problems and typical student results will be presented daring the
conference*

Sample Problem il

Purpose: To test the mode, median and mean for stability.

Question 1: Which of these measures of central tendency vary most (and least) from

sample to sample?

Question 2: which of these measures is most (and least) stable when they are computed
from grouped data?

Method: Choose tvo of the four random distributions available in PSYSTAT* distribution

uses N 1 s (sample sizes) of 20, 100, and 500 and the following number of intervals:

_N_ i int

20 3 6 8

100 5 10 15

500 10 20 30

That is, for each of the tvo distributions, a minimum of nine machine computations
must be made.

Results: Using the form provided (for each distribution) enter the appropriate sample median,

sample mean, grouped mode, grouped median and grouped mean. Hint: You may want to use
the computer to calculate the grouped median and mean*

Discussion: On the form provided, discuss your results* What can you concLude about the

relative stability of these three measures of central tendency? Are the resalts the
sane for both distributions?

Sample Problem #2

Purpose: To test the effect of significance level and sample size on the accuracy of the one

sample "t" test* The probabilities of Type I and Type II errors will be empirically
investigated*

Method: Type I error is defined as the rejection of a true hypothesis* Type II error is the

failure to reject a fake hypothesis*

1* Use the N0RRAL population (mean = 0) to generate samples of different sizes*
Use T- TEST to test a true hypothesis (Ho) about the population mean* San a
sufficient number of simulations for each sample size so that you can plot the
probability of Type I error as a function of sample size (N) for. each of three
significance levels*

2* Repeat 1, using a faise hypothesis (Ho). Plot the probability of a Type II
error as a function of M for each of three significance levels* Also plot 1 - p
(Type II error) as a function of N for each of your three significance levels*
These last curves are the "power" carves for the "t" test for yoar choice of
hypothesis.

Results: Discuss your empirical curves, what effects should significance level have on

probability of Type I and Type II error? Do your results confirm yoar expectation?
If not, why? what effects should sample size have on these probabilities? Are yoar
results in agreement? If not, why? Are the assumptions underlying the «t" test
violated in this experiment? If so, which assumptions?

516

523

Results

Since there has been only one semester's experience with PSTSTAT, quantitative assessment
of the effect of its use vas not undertaken. Students vere asked to evaluate their experience
and the results of this evaluation are entirely consistent with my own judgment. Approximately
90% of the 87 students felt that using PSTSTAT vas worthwhile for ono or both the following two
reasons:

1. It eliminated concern with hand calculations and computational formulae. <

2. It eliminated the air of mystery surrounding the computer's capabilities amd

In addition, a majority (60%) felt that their comprehension of the course content vas
enhanced by using PSTSTAT and that the simulation experiments vere worthwhile. The remaining 40%
either found no value at all in the computer exercises or vere equivocal in their response.

On the negative side, complaints vere mostly due to the nature of batch mode operation:
excessive tine spent in wasted trips to the computing center (long turn-around) and long waits
at the keypunches. There vere also the unavoidable complaints about down time. The use of remote
terminals will hopefully reduce soae of these problems and these are being included in future
plans.

The current cost of using PSTSTAT in the batch mode is quite low. The 87 students in the
class each used an average of 5 minutes of machine time (188 360/65) during the semester with an
average cost of S20 per student per semester. This figure will hopefully be even lover when
planned improvements in PSTSTAT's efficiency become implemented.

1. Koh, Y. 0., "The computer is an instructional tool for the statistics course," proc.

Conference on Computers in the Undergraduate Curricula, 1970, pp. 2.4-2.17.

2. tfikoff, R. L. , "Using the computer in basic statistics courses," Proc. Conference on

Coapu ters in the Undergraduate Curricula, 1970, pp. 2.18-2.24.

3. Sandusky, A., Campos, F., Livingston, J., Love joy, E.P., Messick, D. M. , ’’Instruction in

Statistics: A Report on the Computer Laboratory for Analysis of Data in Psychology.” Proc.

Con ference on Compute rs in the Undergraduate Curricula, 1971, pp. 429-436.

functions.

REFERENCES

. v

52 4

A COURSE 01 COHP0TING AID STATISTICS FOR SOCIAL SCIENCE STUDENTS

Herbert L. Dersben
Hop# College
Holland, Hichigan 49423
Telephone: (616) 392-S1 11

2£iais ai tkt £ma

Before the introduction of the course to be described in this paper, nost econonics and
social science students at Hope College enrolled in two nathenatics courses. These vere
introductory statistics and cnnputer programing. In the acadenic year 1969-70 two developnents
occurred which pointed to the advisability of conbining these courses.

First, Dr. Jay Folkert conducted experinental sections of the introductory statistics
course at Hope College in which he used the cosputer as a tool to obtain illustrative
infornatioa. He did this by allowing students to use previously written progress on prepared
data decks. This was done in conjunction with the project tc jtudy i^e use of the conputer in
statistical instruction sponsored by the Rational Science Foundation and the University of North
Carolina, in which Dr. Folkerrt was a participant. At the close of the experinent it was Dr.
Folkart's feeling that the conputer was an asset in such a course but that sonething was lost
because the students vere not able to participate in the preparation of the programs.

At the sane tine, a coursa on conputing for social science students was introduced into the
Hope curriculun. This course is basically a FORTRAN programing course. Those who were involved
with teaching this course found that sone knowledge of statistics would be valuable to those
students enrolled, with sone statistics background, the students could be assigned projects
pertinent to their fields of interest.

It was therefore the consensus of the Hope College nathenatics departnent that it would be
nore valuable to conbine statistics and conputer programing into one course for social science
students rather than to continue with two separate courses. A proposal was nade in the t'all of
1970 to the National Science Foundation for the developnent of such a course, in conjunction
with the developnent of a laboratory for the nathenatical probability and statistics course, and
this project was funded.

Value of the Conputer

There are three najor reasons that the conputer is an asset to the introductory statistics
course. First, exposure to the conputer and conputing is a necessary experience for any social
science student. He should ba aware of the econonic, sociological and psychological inpacts of
the conputer as well as the, application of the conputer to the solution of problens in his
discipline.

Second, the conputer can serve as an aid in teaching statistics theory. The student has a
much greater nastery of a concept after he has explained it to soneone else, when a student
writes a progran he is doing just this, explaining to the conputer how to solve the probleu. For
exanple, in the assignnent show in Figure 3, the student is asked to explain to the conputer
how to test hypotheses. Also t.ie conputer can be used to provide the student with illustrations
which further enhance his understanding. An example of this is found in the assignment given in
Figure 2 in which the student is asked to illustrate the normal approximation to the binomial.

Third, the conputer allows the student to apply the statistical procedures he is learning
to useful sets of data, thus giving hin valuable experience in interpreting results and an
interesting incentive for learning the statistics.

Descr ipt^gn of the Course

The course being developed is entitled "Applied Statistics and Conputer Progranning. " The
only prerequisite is high school algebra. It is a two senester course for three hours credit
each senester. An outlise of the topics presented in the course is found in Figure 1*

The students are introducad to a amplified forn of inpat and output so that they can begin
progranning without being exposed to FORBAT statenents. This is done by subroutines written for
this course because Hope College has an IBA 1130 which has no sinplified input/output included
in the systen. The author has prepared notes to serve as a text for the class for the FORTRAN
portion of the course becausn existing texts present the language in a sequence different fron
that deternined to be optinal for this course. For exanple, we present subscripted variables
very early in the course because they are needed to progran exanples and procedures in
descriptive statistics.

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Normal Approximation to the Binomial

Purpose > The purpose of this assignment is to introduce
the student to testing a hypothesis about a sample mean

and illustrate type I and type II errors.

Description Write a function subprogram which has the
following arguments i XMUO, the hypothesized mean, XMU,
the actual mean, SIG the actual standard deviation, and
N, the sample size# The subprogram is to generate 100
samples of ^ize N from a normal distribution with mean
XMU and standard deviation SIG. For each sample, a 95%
confidence interval is constructed assuming sigma known,
and a test is made as to whether XMUO is in the confidence
interval, j.e., whether^ - XMUO is accepted. A count
is made of the number of times the hypothesis is accepted
This is the value to be returned for the function#

Write a calling program which calls this function four'
times, each time with XMU0=20, SIG=5» N-10, and for
XMU=20,22,25.30#

Outputi Your output should consist of XMUO, XMU, SIG,

N and the value of the function for each call of the function.
Questions i l. Relate the results of each call to function
to either type I or type II errors. Specify which.

2# Punch a card summarizing your results.

3. What would be the effect on your answers if SIG were
10 instead of 5? What if N were 20 instead of 10?

What if we used a 99% instead of 95% confidence interval?

40 CornTjute the theoretical probability of making an
error in each of the four performed tests of hypotheses.
Indicate for each whether it is a type I or a type II
error# Compare these with your results.

5. The above, program tests the hypothesis ^=20
against the two-sided alternative /- J 20. How would
your answers be changed if a one-sided alternative
yiA > 20 were used? W*»at ifytf-< 20 were the alternative?

£/ytra things to try > Add enough generality to your
program that you can try some of the things suggested
in questions 3 and 5 above.

Figure 3.# Sample Assignment Testing of Hypotheses

520

527

The statistics text chosen is Bleaantarv Statistics by Paul G.Hoal, and the topics covered 65
follow the presentation of the text with exceptions noted below. Descriptive statistics and 66
probability are reversed in order that the students say gain sone fasiHarity with FOBTBAI and 67
subscripted variables before they are needed for descriptive statistics. Sose discussion is
iuded concerning randoa nuaber generators along with experience in their use when randon 68
sanpling is treated. Also* the students are given practice in using canned subroutines and 69
interpret -rg their results for regression and analysis of variance.

Pive data se ts, each consisting of several variables, are stored on a disk. The students 71
learn early in the course how to access this data. These sets are data actually used for 72
research purposes in the areas of sociology, psychology, education and economics, and have beam 7J
contributed by faculty on the Hope caupus fron their research and fron other books and articles.’
Already three additional sets have been contributed for next year. Bach student is assigned ona 74
data set and one variable fron that set which he uses throughout the year. This use ranges fro* 75
finding the naan and standard deviation to taking randoa saaples to obtain confidence intervals 76
to correlation and regression with other variables in the sane data set.

The students work fewer textbook problens than in the standard statistics course. Instead, 78
they write coaputer prograas for solving these problens and then apply these prograas to their 79
daba sets. The students are given a total of 25 assignments involving the coaputer throughout 60
the year. This averages out to. slightly less than one assignaent per week. The assignaents
typically involve the writing of a prograa, the application of that prograa, and the answering 81
of sone questions intended to bring out the iaportant points. In aany cases students are asked 82
to puuch cards suasarizing their results so that a aean result nay be obtained for the entire 83
class. Extra credit problens are given along with each assignment to challenge the better
students. Two saaple assignaents are found in Figures 2 and 3. 84

The project for developing this course is of two years duration. In the suaaer of 1971 this 89
course was organized with the assistance of four senior aatheaatics aajors who wrote the 90
necessary subroutines and programing examples as well as testing tho coaputer assignaents. The 91
coarse is being taught for the first tine in the acadeaic year 1971-72 with a starting
enrollaent of 26 students. The suaaer of 1972 will be devoted to revising the course according 92
to the experience gained during the preceding acadeaic year. The course will then be taught in 9J
rerised fora during the acadeaic year 1972-73 and the following suaser a final report will be 94
made along with the final preparation of materials such as course outline, lecture notes and
assignaents. These saterials will be distributed to allow other staff aeabers to teach the 95
course.

At this writing it Is the aiddle of the first year of the project and hence too early for 100
iny fira discussion of results. Thus far the reaction of the students has been nost favorable. 101
i>oae have indicated that they feel the statistics is aade easier to understand by the use of the i02
coaputer. I suspect, however, that there are others for whoa the coaputer siaply clouds the
issue. Nora students' have bean completing the extra credit portion of the assignaents than was 103
expected.

The author feels that the norale and interest of the students are such greater in this 105
course than in either of the two parent courses, and for this reason, the course is a pleasure 106
to teach. TheLe has also been a favorable response to this course fron our social science 107
faculty who feel it is a nost valuable course and are encouraging their students to take it as
well as assisting us in its developaent. 108

pgsstieiigB g£ tie Liaiast

528

AN ALTERNATIVE APPROACH

TEACHING STATISTICAL HETHODS
S. C. Via

California State Polytechnic college
San Luie Obispo, California 93401

An undergraduate course in statistical sethods is generally a non-aa thesatical exposition
of the theory of statistics* The statistical techniques covered in such a course are sostly, if
not conpletely, based upon the nornal theory. Because the norsal distribution is a continuous
distribution, as in-depth study of the distribution necessarily requires the background of
calculus. Hence, in a pre-calculus sethods course, even the sisplest techniques based upon the
norsal theory cannot be rigorously justified. Consequently, it is difficult for the students to
grasp nose of the isportant statistical concepts and to understand the lisitations in applying
the norsal theory. These difficulties cannot be cospletely elisinated without relying on the
concept of the randosization theory.

The randosization concept and the theory of significance tests based on it appear to be
entirely the results of R. A. fisher's search for the underlying principle of experisental
design (1926). The ideas involved are very sisple. The null hypothesis, used in all treatsent-
cosparison experinents, is that there are no differences of any kind in the effects of the
various treatments on the responses of those experisental units under study. If this is held to
be true, and if the treatsents are assigned readonly to the experisental unit, then all possible
associations of treatsest labels and experisental-unit responses are equally probable, ror every
association, one can calculate (at least conceptually) the chosen test statistic and derive its
distribution fros the equally probable associations. Then it is a sisple natter to calculate
fron this distribution the probability of any outcose as favorable or less favorable to the
null hypothesis as the one observed. This is the significance probability.

A sisple worked exasple of the randosization test can be sade using the data fros G. V.
Snedecor's (1956) Ststia^iqql flethodq* Two preparations of the Hosaic virus were tested on leaf
nusber 8 of eight different plants. Each test leaf represented a pair of sanpling units,
separated by the leaf aid rib. Treatsents were assigned at randos within responses. The data
were:

Lesions per Half Leaf

Plant nusber

Mean

Preparation A

Preparation B

A-B

-1

If the null hypothesis of no differential effects of the virus preparations on the production of
lesions is held true, then this is but one of 28 * 256 equally probable, possible sets of
differences. Those equally favorable to the null hypothesis and shoving an excess of lesions for
preparation A are:

and that one less favorable to the null hypothesis is

1 6 13 14

1 3

1 -1

1 1

These four and their synsetric cosplesents obtained by switching labels A and B on each and
every leaf are the eight possible osteoses which deviate as such or sore fros the null
hypothesis as does the outcose actually observed. Thus, the significance probability is 8/256
= .031. Under the null hypothesis, the probability of observing a difference as such or sore
than the difference actually obtained is snail (.05 is the usual critical significance
probability), so we place in doubt the hypothesis of no differences between the two
preparations of the Mosaic virus. Thus, the test is justified step by step. A sisple paired-
cosparisons t-test based on the nornal theory gives cosputed ( t c) * 2.63 and significance

probability of

P(|t(7)| > 2.63) = -034 -

522

529

The agree lent between the two ways of calculating significance is reaarkable. In fact, since

is a aonotone function of

x, x < x’
Pndt

(7)

if and only if

> 2.63) - .031

t < t»
c c

, ve nay write

PN(|t(?)| > 2.65) = ,03't

where ft and ft atand for: "derived fron the randonization distribution induced by randonization
of treatnents to eiperiaental units" and "derived fron saapling independent identically
distributed noraal responses." Since the derivation of the t-distributioa and the conputation of
significance probability are far beyond the scope of an undergraduate course in statistical
nethods, the t-test cannot be rigorously justified. Another good feature of the randonization
theory is that the role of randonization in ezperiaental design becones clear. On the other
hand, should all conditions for a valid test based on the noraal theory be satisfied, the
randonization procedure in an ezperinent can be onitted. ♦ Hence, within the fraaework of the
noraal theory, it is eitrenely difficult to explain the role of randonization. According to the
randonization theory, it is also easy to show why a snail sanple cannot provide enough
infornation for a valid test. For instance, if a sanple of size two is used to test a hypothesis
about a aean, the saallest possible significance probability is 2~2 * .25 which is nuch too
large to be regarded as significant. Siailarly, the snallest possible significance probability
for testing hypothesis about equal aeans in a 3 x 3 Latin sguare design is .5. However, within
the fraaework of the nornal theory, it is difficult to show that these tests nay be totally
invalid.

Currently, the randonization test is seldon taught in a statistical nethods course because
it is not easy to evaluate Pr in general. Each tine a randonization test is used, the
critical region nust be deternined on the basis of the data which were collected. To describe
the degree of difficulty involved, consider an analysis of variance problen with 8 treatnents, 2
blocks and 8 plots per block. For these, the possible ways the treatnents can be assigned to
plots nunber (8.*) 2 • Since (8.*)2 is in excess of 1.25 x 109 , it is not feasible to
enunerate all possible assignnents of treatnents. Without a high-speed coaputer, the
application of the randonization test is United to extrenely siaple problens. Using a high-
speed conputer, one can sanple (Honte Carlo) the population of possible randonization 1000 tines
with replacenent and calculate sanple estinat es of significance probabilities. Errors
attributable to this saapling have a binonial standard deviation

{

p(l-p)

1000

V p(i-p)
31.62

In the range of p, usually regarded as significant (p < .03) , this is at nost .006891 and,
hence, of slight practical concern. The naxinun of the standard deviation is .01581 which occurs
at p - .5, a value of no practical interest in testing hypotheses. Thus, the application of the
randonization theory is broadly extended. The standard deviation of the estiaator is always a
constant divided by the square root of the sanple size. As the sanple size increases, the error
attributable to this saapling decreases. A worked exanple of the flonte Carlo nethod applied to a
three-factor factorial design with replicates (subsanplings) was given by tfu and Vi Ilians
(1971).

The idea behind the sinulation is essentially the estination of a proportion of a binonial
population. Since estinating a proportion represents a class of inportant problens which are
usually covered even in a statistical nethods course at lower division level, sinulation
introduces no new concepts. High-speed conputing has gradually becone an integral part in
teaching statistics. The use of a conputer in sinulation will not create any additional
difficulties. Perhaps it is to the advantage of the students to expose theaselves to high-speed
conputing at the earliest possible tine.

It has been shown, generally, by Urquhart (1965) that the significance probabilities
derived fron randonization tests are well approxinated by the significance probabilities derived
fron noraal theory. Hence, the usual statistical nethods can be introduced as approxinations to
randonization tests. The new approach has the theoretical elegance of the randonization theory
and retains conputational simplicity of the tests based on the nornal theory. At present, the
randonization theory still cannot replace the noraal theory in an undergraduate course in
statistical nethods because of high cost of conputer tine, but it can certainly supplenent the
nornal theory. It is well known that, if any of the conditions for a valid test based on the
nornal theory is not satisfied, the consequence nay range fron low power to grossly invalid
test. When in doubt, one should use the randonization test instead of a test based on the nornal

ERIC

533

530

theory* The randomization test is a 1 on parametric test but, unlike other nonpar ametric tests,
it is a powerful test. According to Lehman and Stein (1949) aad Hoeffding (19S2), the asyaptotic
relative efficiency (A. B. E.) of a randomization test is 1.0 when compared to the most powerful
parametric testa in soae specific situations.

In conclusion, it is shown that the randomization theory can be easily incorporated into a
statistical methods course. Many advantages of the simple theory make the short time required
to cover it worthwhile. Using this new approach la teaching, the pioneers can expect some
resistance from the students because no adeguate textbc oks or reference books are available, and
the randomization theory is in addition to the standard methods that must be studied. However,
the resistance will diminish as the new approach becomes widely accepted and the students see
the advantages of the new approach.

B EFEBENCES

1. Fisher, B. A. (1926). ■The arrangement of field experiments.* Jgpf. Ministry Auric. * 33,
503-513.

2. Hoeffding, W. (1952). "The large-sample power of tests based on permutations of
observations." The Annals Mathematical Statistics. 3b,369-400.

3. Lehmann, B. L. And Stein, C. (1949). "On the theory of some nonparametr ic hypotheses." The
Annals of Mathematical Statistics. 20, 2B-45.

4. Snedecor, 6. v. (1956). St^istiq) Methods. Iowa State College Press, Ames, Iowa, 49-51.

5. Urquhart, V. S. (1965). "On the permutation distribution of a multivariate test statistic."
Ph.D. dissertation, Colorado State University, 106 pages.

6. Mu, s. C. and Williams, J. s. (1971). "Randomization test for factorial designs."

Ecagfladiaae °£ j&i Zit&h iaaaal aiigggiiu as its ifllaalasa. a£ saieasst Ssisasa

Sfatistjc?. Oklahoma State University, Stillwater, Oklahoma.

5 1

INDIVIDUALIZED INSTRUCTION IN BASIC STATISTICS:
AH EXPERIMENT IN COMPUTER MANAGED INSTRUCTION

Frederick S. Halley
State University of New York
Brockport, New York

lilt £od uc t _i on

The purpose ci this paper is to describe how computer batch processing was utilized in the
development ot a programmed self instr uct iona 1 course, its costs, student evaluation ot the
instructional method, and future plans for the continuation and development of computer managed
sell instruction.

During the past three years, a team of instructors at S.U.N.Y. Brockport have been
developing and applying a programmed self instructional tecnnigue to the teaching of basic
statistics which presents a significant departure from the usual lec t ur e/d iscuss ion method of
instruction. The technique surrounds students with all of the necessary resources to master
course objectives and turns them loose to do it on their own without traditional classes. In
this manner, students are required to become active participants m the learning process and nay
learn by doing the activities they are usually only told about in traditional classroom
situations. The improvement and individualization of instruction is made Possible by the use of
computer technology m the management of instruction.

Descrj £t i on oi trie Course

The structure of the course presents a maximum amount of freedom tor the student. The
student may select from several alternatives to meet the requirements of the course. His only
requirements are to turn in homework assignments and pass a final examination. Materials
available to the student for use in meeting course requirements include a self-study guide, a
prog ram iTied statistics text, homework assignment sheets, an individualized set of data, audio
notebooks and accompanying visual aids, and a statistics laboratory equipped with calculators,
"onework assignments, due periodically during the semester, set a minimum speed at which
students* work progresses. Nothing prevents a student from expediting this work to complete the
course ahead of schedule. Students have taken the final examination as early as midsemester.

The student study guide provides learning parameters tor the student as well as
instructions tor learning. In the study guide {Nasca, Potter and Halley, 1971) there are twelve
units, each with a homework assignment. Each unit states behavioral objectives which the
students should be able to accomplish after completion of the unit, a summary of principles and
concepts used in the unit, examples, and references to other available instructional materials,
such us programmed texts, audio notebooks, and transparencies. The units cover levels of
measurement, central tendency, variability, score transformations, the normal curve, sampling
distributions, the t-ratio, correlation, regression, prediction and chi square. The study guide
is not intended as a substitute for a text, but rather a device to provide direction to the
student in his endeavor to learn statistics.

For each unit, the student is provided with a homework sheet which contains exercises
specific to the unit. It requires the student to demonstrate accomplishment of the behavioral
objectives of the unit by applying the principles and concepts of the unit to his own
individualized set ot data. While each student has the same assignment, different sets of data
prevent plagiarism.

The study guide refers students to specific sections of tour programmed statistics texts.
Students are encouraged to buy one of the programmed texts (Amos, Brown and Mink, 1965, Elzey,
1971, McCollougn and VauAtta, 1963 or Smith, 1970), but are also encouraged to use other
programmed texts if one is not sufficient. To make this practical for students, copies ot each
are kept on reserve at the college library.

In addition to the study guide and programmed texts, students have audio notebooks and
transparencies to aid them in learning the materials of the course. Some of the tracks on the
audio notebooks deal with mechanical matters such as the use of the calculators. Most ot the
audio notebook tracks are intended to be used with transparencies which illustrate statistical
conceots. By overlaying transparencies, differences in distributions can be illustrated, curves
can be compared and regression linos can be placed in sea t t ergra ms.

Programmed self instruction allows the superior students to finish the course without the
aid of instructors or laDoratory assistants before the end of the semester, thereby enabling
instructional efforts to be expended as individualized aid for students having difficulty

533

mastering course materials. The statistics laboratory is open se veu t y-to ur hours per week with
laboratory assistants present. It is equipped with 20 electronic calculators. Faculty
instructors are available in the laboratory for sii hours per week. Under these conditions, more
highly individualized aid is given to students who need help than could normally have been
provided under traditional classroom conditions, while at the same time, sparing students who
are able to work independently on their own the possible boredom of traditional classroom
lectures.

One major problem extant in
the tendency tor students to plagia
student's homework problems were
had the same set of data and the sa
answers. This lead to students
themselves can be pcdagogica lly hel
defeated the purpose of a self
student cooperation. It was observe
from their instructors. Put it was

the course before the application of compu
rize each others' homework. This was possi
based on data printed in the study guide,
me homework assignments, each was expected
copying each others answers. While student
pful, the mere copying of each others' answ
study course. However, it was deemed des
d that often students could learn more from
also desirable to prevent copying of each o

ter technology was
ble because each
Since all students
to have the same
cooperation among
ers was not. This
irable to preserve
each other than
thers' answers.

Individualizing a different set of data for each student's homeworx assignments, without
the aid of a computer, would have required laboratory assistants to calculate each student's
homework before correcting it, a very formidable task. Through the use ot a computer,
individualized data sets plus answers to homework problems could bo easily generated, thereby
eliminating the temptation of merely copying from another student, but at the same time,
preserving the possibility of students cooperatively sharing a mutual learning experience.

The Use of the Computer in Developing Individualized Data Sets and Homework Answers

Initially it was planned to generate a separate set of data tor each student. However, it
was later decided that pedagologica 1 advantages could be gained by establishing large population
and then selecting student samples from the population. This provided the rare opportunity to
show students the relationship between a population and a sample and to illustrate the concepts
of sample variation, sample error, parameter and statistic.

The first problem in developing a population was the securing of data,
previously collected data from 1,000 Midwestern college students which provided
for 5 of the variables students used in completion of homework assignment
remaining variables used in the homework assignments were not empirically avai
computer was used to simulate data for seven more variables. Simulated variables
in such a way that certain population parameters would be insured. For instance,
the population was urban, 55 percent was suburban, and 15 percent was rural
generated with a slightly better (but statistically significant) High school Rege
Freshman G.P.A.'s were simulated. Likewise, a relationship between place of birt
siblings was buil't into the data.

The author had
data suitable
s. Data for the
lable, so the
were generated
JO percent of
• Females were
nts Scores and*
h and number of

A punched card file of 1,000 data cards
a data base from which random samples of 50 i
class. The data base was read on to a random
to select samples of 50 cases from the file a
both for the printing out of each student's s
use and as a data file for the computation of

with

the

po pu

lation lat

a wa

ndi vidua

Is we

dra wn

for

access

f ilc

and

a rand

om n

nd wr

ote

them

magne t

ic t

et of

ta on

indivi

dual

each

s t

ude nt

' s

homewor

k as

s produced and
each studen
umber ge n e r a to
ape. The tape
data sheets f
sign me nt •

ser
t i
r wa
was
or s

ved as
n the
s used
used

t udent

A program was written to print out the entire population card file so that it could be
displayed on a tackboard in the Statistics Laboratory. The format was similar to that ot the
students' data sets so the students could readily see the source of their sample. This enabled
the student to compare his sample to the population. To allow statistical comparisons, the
population parameters were computed and posted.

Once the student data sets were established, it was only a matter of programming the
homework assignments. The general philosophy in designing the programs that calculated the
students' homework was to compute the statistics in the same manner in the computer as the
students were using calculators in the laboratory. This made it possible to print out critical
computations (i.e. means, sums of squares, expected frequencies, et.c.) so that output could be
used for diagnostic purposes as well as for correction of homework. A few departures were made
from this approach. For instance, in tests of significance, sampling distributions were computed
rather than looked up on tables.

534

Con£Ujjer costs £o£ De vo 1 opien t aria Operation

The computer costs must be divided into two categories: first, the cost of development
which includes machine time for drafting and developing programs, and second, the cost of
operation which includes only the tiae for running programs which have been debugged.

The developmental costs of the FORTRAN programs which were required to do the eleven
homework assignments as well as to generate and print sample data were $109.75 on an I.e.R.
360/65. These were one time costs and are not incurred on subsequent utilization of the programs.

The operation costs are dependent on the number of students for whoa data and answers are
being generated. For 300 students, the cost of individualized materials was $.36 per student.
The greater the number of students, the less the cost per student. This includes the students'
individualized data sheets and answers and intermediate computations for eleven homework
assignments.

Mack ine Requirements

While an IBM 360/65 was used for this application, a much smaller machine could be used.
The maximum core requirements tor any program used on the 360/65 was 56K bytes or 1 4K words. The
advantage of the 360/65 over many smaller machines was the ease of programming available in the
extended 360 FORTRAN IV and the ease of creating and accessing data files.

The system of programs used a large tape file which contained the sample members for each
student's data set. Tape facilities for such mass data storage are available on most college
computer facilities. However, it would be possible to use a much smaller system without tape
facilities, such as I.B.M. 1130, if one would be willing to give up the programming conveniences
of an extended FORTRAN and use a more compact student sample storage techniques. Storage
requirements could be reduced if only record numbers of student sample members were stored and
student samples were reconstructed from the population each time it was needed by a homework
prog ram.

Student Eva luatjon of course

A brief questionnaire was distributed among students so that student evaluation of the
items were included as indicators of whether or not students' reactions t.o the course were
favorable. Of approximately 300 students, 141 returned questionnaires.

One of the items used to ascertain overall approval of the course was the question, "Would
you recommend this course to a friend?" An affirmative response indicated approval of the course
and a negative response indicated disapproval. Sixty-two percent of the students indicated they
would recommend the course to a friend, 35 percent indicated they would not. Two percent made no
response (see Table 1). Clearly, a majority of the students approved of the course enough to
recommend it to a friend.

Number Percent

Would recommend to a friend 88 62

Would not recommend to a friend 50 35

No response 3 2

Total 141 100

TABLE 1. Recommendation of Course to a Friend

However, approval of the course may not be a result of the techniques used (i.e. , computer
managed instruction and self instruction) but rather the subject matter itself. As a further
indicator of approval of the instructional techniques, students were asked if they would like to
have other courses taught in the same format. As indicated on Table 2, 61 percent answered
affirmatively, while 37 percent answered they would not.

535

S','7

Number Percent

Would like other courses In seme format 86 61

Would not like other courses In same format 52 37

No response 3 2

Total 141 100

TABLE 2. Preference for Other Courses in Same Format

Because of a concern that many students sight feel isolated in a selt taught computer
managed course, an attespt was made to seasure to what degree students thought the course was
personal. While the potential for isolation exists, there also exists the opportunity tor high
personal involvement in the course which could offset feelings of isolation. To measure the
degree of personalness expressed by students, a Likert type scale was given to students tor
their response on the evaluation questionnaire. Students were asked, "For you, did not having a
regular instructor in a traditional class make the course impersonal?" Five responses were
presented to students. They included, "Yes, very impersonal," "Only a little impersonal," "It
was just as personal as my other courses," "Somewhat personal," "No, it was very personal,"
Twenty-three percent of the students responded that the course was very impersonal, another 2b
percent indicated that it was only a little impersonal. Twenty-two percent indicated that the
computer managed self study course was just as personal as their other courses. Nine percent
indicated that it was somewhat personal and 18 percent indicated that the course was very
personal. (See Table 3.)

Response

Number

Percent

Very Impersonal

A little impersonal

As personal as other courses

Somewhat personal

Very personal

No response

Total

141

100

TABLE 3, Personalness of Course

Probably what docs make the course personal for some students is the degree that they may
become personally involved in the course and the degree to which they may pursue their own
interests within the context of the course. While the data is not capable of supporting it, the
writer suggests that the degree to which a course becomes personal is related to the degree to
which a student can pursue his own interests through a choice of optional Leans tor fulfilling
the requirements of the course.

Many options could be built into the self instructional course. Optional homework
assignments could be designed so that you would use discipline specific data. Students could

528

536

ERIC

select fora several homework assignments to fulfill the assignment for one unit. For example, in
the test unit, students would be given the option to select income variables (Economics) ,
academic difference variables (Education), mobility variables (Geography), or status variables
(Sociology) to fulfill the homework assignment.

A computational option could be added to the course. Students now are reguired to complete
the statistical computations on desk calculators. Several students indicated on the evaluation
questionnaires that they knew how to use a compu ter and that use of the desk calculators was
"busy work." For these students, the option of using a computer (desk top or larger) could be
provided. To nake this option a real choice, as well as providing the student with an
individualized computer data printout, those that elect the computer option could be provided
with a copy of his data punched in IBM cards.

To give the student a greater sense of control over the course, an interactive
computational system could be employed to correct and grade students* homework. (See "Plans tor
Future Development.") In this manner, when a student was ready to have his homework checked, he
could sit down at the teletype terminal and enter his answers. The computer would return
corrected answers, diagnostic information, and record the student's performance in a
computerized grade book. This would negate the necessity of turning in homework and waiting for
a grader to correct it. No grading delays would prevent the student from progressing at his own
pace and reinforcement would be nearly instantaneous. Moreover, personnel now involved in
grading would be freed to give individual help to students in the statistics lab.

Plans for Future Development of Com pu ter flan agegent

In batch node, the degree to which further individualization can continue is limited. Batch
mode processing requires that all the homework be computed at once. Students must wait until
laboratory assistants correct their work to proceed to the next assignment. In some cases, this
impedes the student from progressing at his maximum speed. A partial solution to this problem
would be to print out two copies of each set of homework answers and diagnostics. One set could
be arranged for easy reference for the graders; a second set would be returned to the student
witn his corrected homework for diagnostics. Presently, the same set of answers are used for
orrection by graders and diagnosis by students. It is impossible to make .his information
'ailable to students in the statistics laboratory before the homework assignments are due.

Such a
de, some t/p
< i c h the st

ssignoent the
listr ibution.
a student migh

system would still delay the e
es of homework problems cannot
udent is required to make a
student was expected to s
It would have been impractical
t select and print out frequenc

valuation of the students* work. Moreover, in batch
be handled. This is particularly true in those
judgmental decision. For instance, in one homework
elect his own class interval for a frequency
to try to anticipate every possible class interval
y distributions for each of there.

The best solution to handling the problem of quick correction of assignments and the
evaluation of problems involving student decision, is to convert the approach to an interactive
computiug system rather than a system which operates in batch mode. Students could then get
correction routines for each homework unit stored in the computer. In this manner, decision pro-
blems could take student decisions as input for parts of the correction procedure.

If an interactive computer system was used, a grade file cou
contain records of the students* homework performance. In short, a
would become the equivalent of an instructors grade book. The gra
time a student called a correction routine for his homework. Simple
for instructors which would list student progress in terms of
performance in those units. Such information could be used by inst
who were having problems with the course so they could be s
attention.

Id be established which would
grade file in the computer
de file could be updated each
programs could be devised
homeworx units attempted and
ructors to identify students
ingled out for individualized

Such a system would require rigid security. Students would be tempted to try to receive
credit for the course without doing the work. For instance, precautions would have to be taken
to prevent a student from calling out a homework correction program, inputing answers that he
knew were wrong, receiving correct answers and diagnosis, and then calling out the program again
to input computer generated correct answers. Similarly, precautions would have to be taken to
insure that students did not have "ringers" take the course for them or calculate their
homework.

The establishment of grade files would also make possible the institution of individualized
testing. An extensive pool of test items has already been developed. By bringing together grade
files and a pool of questions over different areas of the course, an individualized final exam
for each student could be developed which would cover the student's weak areas. Students could
be told that they would only be tested over their mistakes in their homework. If they made no
mistakes, they would receive no final exam and would only be graded on homework performance

537

(which would be perfect). If they wanted to know what they would be tested on, they could be
told to keep their teletype printouts as records of their nistakes. Pron an instructional point
of view, either way, the students learn the naterial.<

In conclusion, the application of the computer has improved the quality of instruction in a
programed self instructional sanple. The utilization of the instructional technique has been
well received by students and does not seen to seriously degrade the studentsf sense of the
personalness of the course. The continued developnent of this technique through the use of
interactive conputer terninals will enable the incorporation of optional ways the student nay
neet the course requirenents thereby enabling hin to tailor the course to neet his own needs and
interests.

REPEBENC*?S

1. A nos. Jinny P. , Poster Lloyd Brown and Oscar G. Mink. Statistical Conce£ts, A Basic

P yog pan. New York: rfarper and Bow, 1965.

2. Elzey, Preenan P. A Progcanned Introduction to Statistics. Belnont, California:

Brooks/Cole, 1971.

3. HcCollaugh, Celeste and Loche VanAtta Statistical Concepts, A Erograa tor Self Instruction.
New York: HcGraw-Hill, 1963.

4. Nasca, Donald J. , Robert Potter and Prederick Halley A Guide to the Study o£ Statistics.

Brockport, New York: Departnent of Educational Research, State University College at

Brockport, 1971.

5. Snith, Hilton G. A Simplified Guide to Statistics for Psychology and Education. New York:
Holt, Rinehart and Winston, 19.70.

530

538

THBOOGH HOLTIPLE REGRESSION AND THBEB-UAT £ N 2 V
IN SOPHOHOBE LEVEL APPLIED STATISTICS FOB THE BEHAVIOBAL AND NATURAL SCIENCES:

Instructor-Student Demonstration of the Harchant Cogito 10 16PB+10TA-2

Clark I. Guilliams, Author
Bobert Fletcher, Student
Hissouri Southern State College
Joplin, Hissouri 64801
Telephone: (417) 624-8100

Introduction

The object of this deaonstration is to introduce instructors of applied statistics or
experimental labs in the behavioral and natural sciences to the Harchant Cogito 10 16PR*IOTA-2.
The author's set for the presentation will be that of an iustructor who teaches "Applied
Statistics for the Behavioral and Natural Sciences" to sophoaore level students. The student
prerequisite is only high school algebra, or equivalent training* Eaphasis is placed on the
analysis and interpretation of student collected data (see Appendix I for the actual behavioral
objectives presented the student on day one of course)*

As a manually operated calculator, the 1016PR combines tve speed asd quietness of
electronics vith the simplicity and easy-to- learn operation of desk-top tape calculator.
Accuracy is assured by factors and answers being printed on the tape vith easily recognized
symbols for their identification* The logical arrangement and markings of operating controls
also contributes to optimum accuracy*

As a programmable calculator, the 1016PB offers some of the capabilities and the
versatility of a small computer-all in the same compact, thirty-five pound desk-top unit. A
program of up to 100 steps may be recorded, remembered, and automatically repeated. The
unconditional and conditional branching features of the Cogito 1016 PR makes it attractive for
programming courses also*

Vhen the 1016 PB is combined with an optional IOTA-2 or -3 unit (Input-output Tape
Accessory) , programs can be recorded on magnetic tape and stored for later use*

The IOTA-2 makes it possible to store up to eleven 100-step programs in one cassette; and
the IOTA-3, which we do not have, is basically the same as the -2, except one can dial the
particular 100-step part of the tape he wishes. However, the time saved with the -3 is
negligible; but it does facilitate identifying short programs on multi-step cassettes.

A library of small tape cartridges can be developed so that any frequently used program may
be transferred from tape to the program memory of the 1016PB in just five seconds.

The 1016PB is algebraically correct in all mathematical operations. The SIGN Key permits
the entry of negative numbers* All factors and results print vith the correct sign. All answers
automatically print with the correct decimal point if keyboard entries are indexed with a
decimal.

After the Cogito prints an answer to any calculation, the result is always transferred back
to the Keyboard Register* This provides a link between all the registers and eliminates any need
to copy or re-enter immediate answers. Each of the six registers can contain up to 17 places,
but only 14 digits will print* However, this is like 99 trillion plus.

TtPicai camaa eiafetes

Suppose we are interested in examining the influence of three new and related drugs on the
EEG activity of two diagnostic categories of rats (e«g., experimentally induced mania or
depression). These data might well be cast in a tvo-by-three (2 x 3) matrix as in Table 1 below
(the scores in each cell are individual EEG frequencies per second- highly improbably, but makes
for dramatic results when interaction effects are to be emphasized).

4k£

539

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Full text of "ERIC ED066875: Proceedings of the 1972 Conference on Computers in Undergraduate Curricula."

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